Complete Test Bank Probability Chapter 7 - Final Test Bank | Applied Calculus 7e by Hughes Hallett. DOCX document preview.

Back to Product

Complete Test Bank Probability Chapter 7

Applied Calculus, 7e (Hughes-Hallett)

Chapter 7 Probability

7.1 Density Function

1) A density function for the daily calorie intake of a certain species is given in the following figure.

A. Find the value of c.

B. What percent have daily calorie intake between 20 and 40?

A line is graphed on a coordinate plane. The horizontal axis is labeled x. The line starts at a point labeled c on the positive vertical axis, moves to the right, and then moves downward to a point labeled 80 on the positive x axis.

A. 0.0125

B. 25%

Diff: 1 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

2) A density function for the age of people enrolled in a class is given in the following figure.

A. Find the value of c.

B. What percent of the class is under 30 years old? Round to the nearest whole percent.

A line is graphed on a coordinate plane. The horizontal axis labeled x in years ranges from 0 to 40, in increments of 10. A point labeled c is marked on the positive vertical axis. The line starts at (15, 0), slopes upward to the right to (20, c), then moves horizontal to the right to (30, c), and then slopes downward to the right to (35, 0). The line between (20, c) and (30, c) is dark shaded. The positive x axis is dark shaded between (0, 0) and (45, 0). All values are estimated.

A. 1/15

B. 83%

Diff: 1 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

3) A density function for the lifetime of a certain type of frog is shown in the following figure. What is the most likely lifetime for a frog of this type?

A curve is graphed on a coordinate plane. The horizontal axis labeled x in months ranges from 0 to 24, in increments of 4. The curve increases from (8, 0) to a point with x axis value of 11 and then decreases concave up to a point with x axis value of 24, close to the positive x axis. All values are estimated.

A) 11 months B) 14 months C) 16 months

D) 19 months E) 21 months F) 24 months

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

4) A density function for the lifetime of a certain type of frog is shown in the following figure. Which is the frog's lifetime more likely to be between?

A curve is graphed on a coordinate plane. The horizontal axis labeled x in months ranges from 0 to 18, in increments of 3. The curve increases from (6, 0) to a point with x axis value of 8 and then decreases concave up to a point with x axis value of 18, close to the positive x axis. All values are estimated.

A) 9 and 10 months B) 12 and 13 months C) 15 and 16 months

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

5) The following figure gives the density function for the number of hours students spent studying for a calculus exam. What is the largest amount of time a student spent studying?

A curve is graphed on a coordinate plane. The horizontal axis labeled t in hours ranges from 0 to 8, in increments of 2. The curve increases from a point on the positive vertical axis to a point with t axis value of 1, decreases to a point with t axis value of 2, and then increases to a point with t axis value of 3. The curve then decreases concave up to a point with t axis value of 6 and further decreases concave down to (8, 0). The positive horizontal axis between (0, 0) and (1, 0) is dark shaded. All values are estimated.

A) 1 hour B) 3 hours C) 4 hours D) 6 hours E) 8 hours

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

6) The following figure gives the density function for the number of hours students spent studying for a calculus exam. Did a greater number of students study more than 4 hours or less than 4 hours? Answer "more" or "less".

A curve is graphed on a coordinate plane. The horizontal axis labeled t in hours ranges from 0 to 8, in increments of 2. The curve increases from a point on the positive vertical axis to a point with t axis value of 1, decreases to a point with t axis value of 2, and then increases to a point with t axis value of 3. The curve then decreases concave up to a point with t axis value of 6 and further decreases concave down to (8, 0). The positive horizontal axis between (0, 0) and (1, 0) is dark shaded. All values are estimated.

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

7) The following figure gives the density function for the velocities of cars passing a checkpoint on a freeway. What is the most common speed?

A curve is graphed on an x y coordinate plane with equally spaced gridlines. The x axis ranges from 0 to 80, in increments of 10, and the y axis ranges from 0 to 0.06, in increments of 0.01. The curve increases concave up from (46, 0) to (70, 0.065) through (60, 0.025) and then decreases to (80, 0) through (73, 0.062) and (75, 0.04). All values are estimated.

A) 60 mph B) 64 mph C) 68 mph

D) 72 mph E) 76 mph F) 80 mph

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

8) The following figure gives the density function for the velocities of cars passing a checkpoint on a freeway. What percent of the cars drove less than 65 mph?

A curve is graphed on an x y coordinate plane with equally spaced gridlines. The x axis ranges from 0 to 80, in increments of 10, and the y axis ranges from 0 to 0.06, in increments of 0.01. The curve increases concave up from (46, 0) to (70, 0.065) through (60, 0.025) and then decreases to (80, 0) through (73, 0.062) and (75, 0.04). All values are estimated.

A) 20% B) 30% C) 40% D) 50%

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

9) The following figure gives the density function for the velocities of cars passing a checkpoint on a freeway. Which were cars more likely to be driving?

A curve is graphed on an x y coordinate plane with equally spaced gridlines. The x axis ranges from 0 to 80, in increments of 10, and the y axis ranges from 0 to 0.06, in increments of 0.01. The curve increases concave up from (46, 0) to (70, 0.065) through (60, 0.025) and then decreases to (80, 0) through (73, 0.062) and (75, 0.04). All values are estimated.

A) Between 55 and 65 mph B) Between 70 and 80 mph

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

10) The distribution of heights, x, in meters, of a group of shrubs is represented by the density function p(x) (no shrubs are higher than 1.5 meters). Calculate the percentage of shrubs which are between 1 and 1.5 meter(s) high.

A line function, p of x, is graphed on a coordinate plane. The horizontal axis labeled x in meters ranges from 0 to 1.5, in increments of 0.5. The vertical axis labeled fraction of shrubs per meter has a marking 0.8. The line slopes upward to the right from the origin to (0.5, 0.8) and then moves horizontal to (1.5, 0.8). A vertical dashed line is drawn for x equals 1.5.

Diff: 1 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

11) Which of the following could possibly be density functions? Select all that apply.

A) p(x) = 0.1 for 15 ≤ x ≤ 25

B) p(x) = sin x for 0 ≤ x ≤ 3π/2

C) p(x) = ((x) with superscript (2)/100) for 0 ≤ x ≤ 100

Diff: 3 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

12) The density function f (x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. What is the probability that the circuit board will cost more than $10 thousand to produce?

A line function, f of x, is graphed on a coordinate plane. The horizontal axis labeled x ranges from 0 to 10 in increments of 2, and the vertical axis is labeled probability density. The line increases vertically upward from (2, 0) to a point in the first quadrant, and then it decreases to (10, 0).

Diff: 1 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

13) The density function f (x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10.

A line function, f of x, is graphed on a coordinate plane. The horizontal axis labeled x ranges from 0 to 10 in increments of 2, and the vertical axis is labeled probability density. The line increases vertically upward from (2, 0) to a point in the first quadrant, and then it decreases to (10, 0).

A) integral of ( f (x) dx) from (2) to (b) B) integral of ( (1 - f (x)) dx) from (2) to (b)

C) integral of ( f (x) dx) from (b) to (10) D) integral of ( (1 - f (x)) dx) from (b) to (10)

Diff: 1 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

14) The density function f (x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Find the height of the triangle that describes the probability density function.

A line function, f of x, is graphed on a coordinate plane. The horizontal axis labeled x ranges from 0 to 10 in increments of 2, and the vertical axis is labeled probability density. The line increases vertically upward from (2, 0) to a point in the first quadrant, and then it decreases to (10, 0).

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

15) A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f (x) pictured below:

A line function, f of x, is graphed on a coordinate system. The horizontal axis labeled x or exam score ranges from 0 to 100 in increments of 50, and the vertical axis labeled probability density ranges from 0 to h in increments of h. The line increases from the origin to (50, h) and then decreases to (100, 0).

Find the value of the height h of the triangular probability density function.

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

16) A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f (x) pictured below:

A line function, f of x, is graphed on a coordinate system. The horizontal axis labeled x or exam score ranges from 0 to 100 in increments of 50, and the vertical axis labeled probability density ranges from 0 to h in increments of h. The line increases from the origin to (50, h) and then decreases to (100, 0).

What percent of the students would you expect to score below 75 points on the exam?

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

17) Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal.

A line is graphed on a coordinate plane. The horizontal axis labeled x ranges from 0 to 100 and has a marking at 60. The vertical axis labeled p has a marking at b. The line moves rightward from (0, b) to (60, b) and then decreases to (100, 0).

According to this simplified model of the distribution of people's ages in the United States, what percentage of the population is between 0 and 100 years old?

Diff: 1 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

18) Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal.

A line is graphed on a coordinate plane. The horizontal axis labeled x ranges from 0 to 100 and has a marking at 60. The vertical axis labeled p has a marking at b. The line moves rightward from (0, b) to (60, b) and then decreases to (100, 0).

In terms of b (see the graph), find the fraction of the population that is between 60 and 100 years old.

A) 60b B) 20b C) 40b D) 80b

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

19) Using the following figure, calculate the value of c if p is a density function.

A line function, p of x, is graphed on a coordinate plane. The horizontal axis labeled, x has markings at 8 and 12. The vertical axis has a marking at c. The line starts at (0, c), moves to the right to (8, c), and then decreases and ends at (12, 0). A dashed vertical is drawn from (8, c) to (8, 0).

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

20) Each of the following density functions represents the heights of a group of people in a community. Which one most likely represents the heights of a group consisting of only the children in the community?

table ( (I. graphic(Miscellaneous:hh-appli-VE286143023 - A curve is graphed on a coordinate plane. The horizontal axis labeled x in meters ranges from 0 to 2, in increments of 1. The curve increases concave up to some extent from the origin, then increases concave down to a maximum point with x axis value of 1.2 in the first quadrant, and then decreases concave down to (2, 0). All values are estimated.))(II. graphic(Miscellaneous:hh-appli-VG286143023 - A curve is graphed on a coordinate plane. The horizontal axis labeled x in meters ranges from 0 to 2, in increments of 1. The curve increases concave up from the origin to a point with x axis value of 1, then increases concave down to a maximum point with x axis value of 1.6 in the first quadrant, and then decreases concave down to (2, 0). All values are estimated.))(III. graphic(Miscellaneous:hh-appli-VI286143023 - A curve is graphed on a coordinate plane. The horizontal axis labeled x in meters ranges from 0 to 2, in increments of 1. The curve increases concave up to some extent from the origin, then increases concave down to a maximum point with x axis value of 1.2 in the first quadrant, and then decreases concave down to (2, 0). All values are estimated.)) )

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

21) The following figure shows the distribution of the number of hours of television viewed per day by a group of children. Estimate the percent of the children who watched more than 2 hours per day.

A curve is graphed on a coordinate plane. The horizontal axis labeled t in hours ranges from 0 to 5, in increments of 1. The curve starts from a point on the positive vertical axis, forms 9 peaks between the t values 0 and 5, and ends at (5, 0). The peaks of the curve increase until t equals 2 and then start to decrease. The peak values of the curve are at the points with the following x values: 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, and 4.5. The highest peak of the curve is at a point with the x value of 2. All values are estimated.

A) 40% B) 70% C) 25% D) 55%

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

22) Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?

A) p(t) = 2t for 0 ≤ t ≤ 1

B) p(t) = 2 - 2t for 0 ≤ t ≤ 1

C) p(t) = 1 for 0 ≤ t ≤ 1

Diff: 2 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

23) The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. Which figure is the density function?

table ( (I. graphic(Miscellaneous:hh-appli-VP286143024 - A curve is graphed on a coordinate plane. The horizontal axis labeled t in years ranges from 0 to 60, in increments of 10. The curve moves along the t axis from the origin until (4, 0), increases to a maximum point with t axis value of 9, and then decreases to (13, 0). The curve then increases slightly above the t axis peaked at a point with t axis value of 40 before decreasing to (60, 0). All values are estimated.))(II. graphic(Miscellaneous:hh-appli-VR286143024 - A curve is graphed on a coordinate plane. The horizontal axis labeled t in years ranges from 0 to 60, in increments of 10. The vertical axis labeled y ranges from 0 to 1, in increments of 0.2. The curve moves along the t axis from the origin until (4, 0), increases concave up to (9, 0.4) and further increases concave down to (10, 0.8), and then increases concave up to (35, 0.85) and increases further concave down through (60, 1). All values are estimated.)) )

Diff: 1 Var: 1

Section: 7.1

Learning Objectives: Interpret a density function.

7.2 Cumulative Distribution Functions and Probability

1) Suppose p(x) is a density function for a certain distribution and P(x) is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 9 and x = 19? Select all that apply.

A) integral of (P(x) dx) from (9) to (19) B) integral of ( p(x) dx) from (9) to (19)

C) P(19) - P(9) D) p(19) - p(9)

Diff: 1 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

2) Suppose P(x) is the cumulative distribution function for sizes of graduating classes among a group of high schools and P(300) = 0.25. Which of the following are possible statements about P(325)? Select all that apply.

A) P(325) < 0.25 B) P(325) = 0.25 C) P(325) > 0.25

Diff: 1 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

3) The cumulative distribution function in the second graph corresponds to the density function in the first graph.

A bell curve is graphed on a coordinate plane. The horizontal axis labeled x ranges from 0 to 10, in increments of 2. The vertical axis is labeled p of x. The curve starts at (0, 0), moves to the right along the x axis until (3, 0), then increases concave up to a maximum at a point with x axis value of 5 in the first quadrant, then decreases concave up to (7, 0), and then moves to the right along the x axis until (10, 0). All values are estimated.

A curve is graphed on a coordinate plane. The horizontal axis labeled x ranges from 0 to 10, in increments of 2. The vertical axis labeled p of x has a marking at 1. The curve starts at (0, 0), moves to the right along the x axis until (3, 0), and then increases concave up to a point with x axis value of 5 in the first quadrant. The curve then increases concave down to a point with x axis value of 6 in the first quadrant and moves to the right to a point with x axis value of 10 in the first quadrant. All values are estimated.

Diff: 1 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

4) An aptitude test is given to a group of students. Scores can range from 0 to 50. Does the cumulative distribution function in the second graph correspond to the density function in the first graph? Answer "yes" or "no".

A line function, p of x, is graphed on a coordinate plane. The horizontal axis labeled score has a marking at 50. The vertical axis has a marking at 1 over 50. The line moves rightward from (0, 1 over 50) to (50, 1 over 50). A curve function, P of x, is graphed on a coordinate plane. The horizontal axis labeled score ranges from 0 to 50, in increments of 50. The vertical axis ranges from 0 to 1, in increments of 1. The curve increases concave down from the origin to (25, 0.5) and then increases concave up to (50, 1). All values are estimated.

Diff: 2 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

5) The cumulative distribution function for the time to complete a step on an assembly line is given in the following table. What percent of the steps take from 0 to 14 minutes to complete?

t min

6

8

10

12

14

16

18

20

P(t)

0

0.03

0.15

0.21

0.54

0.78

0.86

0.97

Diff: 1 Var: 1

Section: 7.2

Learning Objectives: Find probabilities using density or cumulative distribution functions.

6) Which of the following cumulative distribution graphs would most likely represent the total annual sales of milk?

table ( (I. graphic(Miscellaneous:hh-appli-TR286143018 - A curve is graphed on a coordinate plane. The horizontal axis labeled date has a marking, January, at the origin and a marking, December, to the right of origin. The vertical axis is labeled faction of total sales. The curve increases concave down from the origin to a point in the first quadrant and then increases concave up.))(II. graphic(Miscellaneous:hh-appli-TT286143018 - A curve is graphed on a coordinate plane. The horizontal axis labeled date has a marking, January, at the origin and a marking, December, to the right of origin. The vertical axis is labeled faction of total sales. The curve increases concave up from the origin to a point in the first quadrant and then increases concave down.))(III. graphic(Miscellaneous:hh-appli-TV286143018 - A line is graphed on a coordinate plane. The horizontal axis labeled date has a marking, January, at the origin and a marking, December, to the right of origin. The vertical axis is labeled faction of total sales. The line slopes upward to the right from the origin to the first quadrant.)) )

Diff: 2 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

7) The density function for the height of trees in a forest is given by p(x) = 0.0004(x) with superscript (3), where x is height in meters and the tallest tree is 10 meters. Find the cumulative distribution function, P(x), for this density function.

Diff: 2 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

8) The density function for the height of trees in a forest is given by p(x) = 0.003(x) with superscript (2), where x is height in meters and the tallest tree is 10 meters. Find the probability, to 3 decimal places, that a tree is between 6 and 7 meters tall.

Diff: 2 Var: 1

Section: 7.2

Learning Objectives: Find probabilities using density or cumulative distribution functions.

9) The following figure shows a density function and the corresponding distribution function. Which curve represents the cumulative distribution function?

Two curves are graphed on a coordinate plane. The horizontal axis has a marking b. The vertical axis labeled y has a marking a. One curve labeled 1 increases concave down from the origin to (b, a), and another curve labeled 2 decreases concave up from (0, 1) to (b, 0). Both the curves intersect at a point.

Diff: 1 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

10) The following figure shows a density function and the corresponding distribution function. What is the value of a?

Two curves are graphed on a coordinate plane. The horizontal axis has a marking b. The vertical axis labeled y has a marking a. One curve labeled 1 increases concave down from the origin to (b, a), and another curve labeled 2 decreases concave up from (0, 1) to (b, 0). Both the curves intersect at a point.

Diff: 2 Var: 1

Section: 7.2

Learning Objectives: Find probabilities using density or cumulative distribution functions.

11) The following figure shows a density function and the corresponding distribution function. The drawing is not to scale. What is a reasonable estimate for b?

Two curves are graphed on a coordinate plane. The horizontal axis has a marking b. The vertical axis labeled y has a marking a. One curve labeled 1 increases concave down from the origin to (b, a), and another curve labeled 2 decreases concave up from (0, 1) to (b, 0). Both the curves intersect at a point.

A) 1

B) 2

C) 3

D) 4

E) cannot be determined

Diff: 2 Var: 1

Section: 7.2

Learning Objectives: Find probabilities using density or cumulative distribution functions.

12) The life expectancy of a bug can be approximated by the density function p(t) = 0.1(e) with superscript (-0.1t), where t is time in days. Find the cumulative distribution function, P(t), associated with this density function.

Diff: 2 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

13) The life expectancy of a bug can be approximated by the density function p(t) = 0.3(e) with superscript (-0.3t), where t is time in days. Find the probability that a bug lives between 3 and 5 days. Round to 2 decimal places.

Diff: 2 Var: 1

Section: 7.2

Learning Objectives: Find probabilities using density or cumulative distribution functions.

14) Which of the following could possibly be cumulative distribution functions? Select all that apply.

A) P(x) = 0.1t - 1 for 40 ≤ t ≤ 50

B) P(x) = 1 - cos x for 0 ≤ x ≤ 3π/2

C) P(t) = ((x) with superscript (3)/500) for 0 ≤ x ≤ 500

Diff: 1 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

15) Let p(t) be a probability density which is defined for 0 ≤ t ≤ 1. Could the following be the cumulative distribution function for p?

A curve is graphed on a coordinate plane. Both the axes range from 0 to 1, in increments of 1. The curve increases concave up from (0, 0) to (1, 1).

Diff: 1 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

16) The graph of a probability density function is given. Sketch a graph of the cumulative distribution function.

A line is graphed on a coordinate plane. The horizontal axis labeled t ranges from 0 to 6, in increments of 1. The vertical axis is labeled p of t. The line starts at (0, 0), passes through (1, 0.25) and (3, 0.25), and then ends at (6, 0).

A line is graphed on a coordinate plane. The horizontal axis labeled t ranges from 0 to 6, in increments of 1. The vertical axis is labeled p of t and has a marking 1. The line starts at (0, 0), passes through (1, 0.125) and (3, 0.625), and then ends at (6, 1).

Diff: 2 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

17) A banana plant typically has about 40 leaves that emerge over a period of 238 days (8 months). Younger leaves emerge more rapidly than later leaves. If you randomly select a banana leaf, the probability density function for the month of emergence is given by p(t) = 0.294 - 0.088(1.016) with superscript (t). If you select a banana leaf at random, what is the probability that it emerged in the first 6 months?

A) 0.91 B) 0.23 C) 0.87 D) 0.55

Diff: 1 Var: 1

Section: 7.2

Learning Objectives: Find probabilities using density or cumulative distribution functions.

18) Let P(x) be the cumulative distribution function for the number of credits taken by students at a community college. Some values of P(x) are shown in the following table. What fraction of the students took between 6 and 12 credits?

number of credits

3

6

9

12

15

18

P(x)

0.20

0.32

0.45

0.50

0.81

0.99

Diff: 1 Var: 1

Section: 7.2

Learning Objectives: Find probabilities using density or cumulative distribution functions.

19) Suppose scores from a standardized test measure from 0 to 100. If scores were equally distributed between 0 and 100, pick the graph that best represents the probability density function.

Six graphs. Graph 1 plots a line on a coordinate plane. The horizontal axis labeled x ranges from 0 to 100, in increments of 100. The vertical axis ranges from 0 to 0.02, in increments of 0.02.The line slopes upward to the right from the origin to (100, 0.02). Graph 2 plots a curve on a coordinate plane. The horizontal axis labeled x ranges from 0 to 100, in increments of 100. The vertical axis ranges from 0 to 1, in increments of 1. The curve increases concave up from the origin to (50, 0.5) and then increases concave down to (100, 1). Graph 3 plots a bell curve on a coordinate plane. The horizontal axis labeled x ranges from 0 to 100, in increments of 100. The vertical axis ranges from 0 to 0.02, in increments of 0.02. The curve increases concave up from the origin to (50, 0.02) and then decreases concave up (100, 0). Graph 4 plots a line on a coordinate plane. The horizontal axis labeled x ranges from 0 to 100, in increments of 100. The vertical axis ranges from 0 to 1, in increments of 1.The line slopes upward to the right from the origin to (100, 1). Graph 5 plots a line on a coordinate plane. The horizontal axis labeled x ranges from 0 to 100, in increments of 100. The vertical axis ranges from 0 to 0.01, in increments of 0.01.The line moves from (0, 0.01) to (100, 0.01). Graph 6 plots a curve on a coordinate plane. The horizontal axis labeled x ranges from 0 to 100, in increments of 100. The vertical axis ranges from 0 to 1, in increments of 1. The curve increases concave up from the origin to (100, 1) through (50, 0.25). All values are estimated.

Diff: 1 Var: 1

Section: 7.2

Learning Objectives: Understand the relation between density and cumulative distribution functions.

20) The probability of a plant surviving t days without water is given by integral of ((ce) with superscript (-cx)) from (0) to (t)for some constant c. If the probability of the plant surviving 6 days without water is 0.4, what is c? Round to 2 decimal places.

Diff: 2 Var: 1

Section: 7.2

Learning Objectives: Find probabilities using density or cumulative distribution functions.

21) The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. About what percent of the people in the school are adults?

table ( (I. graphic(Miscellaneous:hh-appli-VT286143024 - A curve is graphed on a coordinate plane. The horizontal axis labeled t in years ranges from 0 to 60, in increments of 10. The curve moves along the t axis from the origin until (4, 0), increases to a maximum point with t axis value of 9, and then decreases to (13, 0). The curve then increases slightly above the t axis peaked at a point with t axis value of 40 before decreasing to (60, 0). All values are estimated.))(II. graphic(Miscellaneous:hh-appli-VV286143024 - A curve is graphed on a coordinate plane. The horizontal axis labeled t in years ranges from 0 to 60, in increments of 10. The vertical axis labeled y ranges from 0 to 1, in increments of 0.2. The curve moves along the t axis from the origin until (4, 0), increases concave up to (9, 0.4) and further increases concave down to (10, 0.8), and then increases concave up to (35, 0.85) and increases further concave down through (60, 1). All values are estimated.)) )

A) 20% B) 40% C) 60% D) 80%

Diff: 2 Var: 1

Section: 7.2

Learning Objectives: Find probabilities using density or cumulative distribution functions.

7.3 The Median and the Mean

1) The heights, in inches, of flowers in a garden have the density function shown in the following figure. How many inches tall is the tallest flower?

A line is graphed on a coordinate plane. The horizontal axis labeled h in inches ranges from 0 to 10, in increments of 5. The vertical axis has a marking 0.2. The line slopes upward to the right from the origin to (10, 0.2).

Diff: 1 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the median of a density function or a cumulative distribution function.

2) The heights, in inches, of flowers in a garden have the density function shown in the following figure. The median height is

A line is graphed on a coordinate plane. The horizontal axis labeled, h in inches ranges from 0 to 40, in increments of 20. The vertical axis has a marking at 0.05. The line slopes upward to the right from the origin to (40, 0.05).

A) less than 20 inches.

B) equal to 20 inches.

C) greater than 20 inches.

Diff: 1 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the median of a density function or a cumulative distribution function.

3) The probability of waiting no more than m minutes for a taxi on a certain street corner is

P(t ≤ m) = integral of ((1/3)(e) with superscript (-t/3) dt) from (0) to (m).

Find the probability of waiting no more than 10 minutes. Round to 3 decimal places.

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

4) The probability of waiting no more than m minutes for a taxi on a certain street corner is

P(t ≤ m) = integral of ((1/3)(e) with superscript (-t/3) dt) from (0) to (m).

Find the median waiting time to 3 decimal places.

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the median of a density function or a cumulative distribution function.

5) The probability of waiting no more than m minutes for a taxi on a certain street corner is

P(t ≤ m) = integral of ((1/3)(e) with superscript (-t/3) dt) from (0) to (m).

Find the mean waiting time.

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the mean of a density function or a cumulative distribution function.

6) Let P(x) be the cumulative distribution function for the number of credits taken by students at a community college. Some values of P(x) are shown in the following table. What was the median number of credit hours taken by the students?

number of credits

3

6

9

12

15

18

P(x)

0.20

0.32

0.45

0.50

0.81

0.99

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the median of a density function or a cumulative distribution function.

7) The density function for lunch time taken by a group of office workers is given by p(t) = 3(t) with superscript (2). The maximum allowable lunch time is 1 hour, so we have 0 ≤ t ≤ 1.

A. Find the median number of hours taken, to 2 decimal places.

B. Find the mean number of hours taken, to 2 decimal places.

A. 0.79

B. 0.75

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the mean of a density function or a cumulative distribution function.; Find and interpret the median of a density function or a cumulative distribution function.

8) The density function for the time to complete a certain task is approximately equal to p(t) = 0.21(e) with superscript (-0.21t), where t is time in minutes and 0 ≤ t ≤ 50.

A. Find the median number of minutes taken, to 2 decimal places.

B. Find the mean number of minutes taken, to 2 decimal places.

A. 3.30

B. 4.76

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the mean of a density function or a cumulative distribution function.; Find and interpret the median of a density function or a cumulative distribution function.

9) The final exam scores for a calculus course were approximately normally distributed with mean μ = 73 and standard deviation σ = 9. The maximum possible score was 100. What is the probability that a randomly selected student received an A grade (90 or higher)? Round to 3 decimal places.

Diff: 1 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

10) The lifespan of a bug is approximately normally distributed with mean μ = 9 days and standard deviation σ = 2.5 days. Assume a maximum possible lifespan of 3 weeks. What is the probability of a randomly selected bug living less than a week? Round to 2 decimal places.

Diff: 1 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

11) The annual rainfall for a desert city is approximately normally distributed with mean 7 and standard deviation 1. Which of the following is the density function for annual rainfall?

A) p(x) = (1/square root of (2π))(e) with superscript ((-(x-7)) with superscript (2)) B) p(x) = (1/square root of (2π))(e) with superscript ((-(x-1)) with superscript (2)/7)

C) p(x) = (1/square root of (2π))(e) with superscript ((-(x-1)) with superscript (2)/98) D) p(x) = (1/square root of (2π))(e) with superscript ((-(x-7)) with superscript (2)/2)

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

12) The annual rainfall for a desert city is approximately normally distributed with mean 8 and standard deviation 1. What is the probability that the annual rainfall will be between 7 and 9 inches? Round to 2 decimal places.

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

13) In the following probability density function, is the mean smaller or greater than the median?

Two curves are graphed in a coordinate system. The first curve rises concave down from a point on the positive horizontal axis to a point in the first quadrant and then it falls concave down to a point on the positive horizontal axis. A similar curve is drawn at a distance from this curve from another point on the positive horizontal axis.

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the mean of a density function or a cumulative distribution function.; Find and interpret the median of a density function or a cumulative distribution function.

14) A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f (x) pictured below:

A line function, f of x, is graphed on a coordinate system. The horizontal axis labeled x or exam score ranges from 0 to 100 in increments of 50, and the vertical axis labeled probability density ranges from 0 to h in increments of h. The line increases from the origin to (50, h) and then decreases to (100, 0).

Do the mean and the median both describe the same point on this probability density function?

Diff: 1 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the mean of a density function or a cumulative distribution function.; Find and interpret the median of a density function or a cumulative distribution function.

15) Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal.

A line function, f of x, is graphed on a coordinate system. The horizontal axis labeled x or exam score ranges from 0 to 100 in increments of 50, and the vertical axis labeled probability density ranges from 0 to h in increments of h. The line increases from the origin to (50, h) and then decreases to (100, 0).

Find the the value of b.

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the median of a density function or a cumulative distribution function.

16) According to data from 2007, the height of five-year-old girls is normally distributed with a mean of 42 inches and a standard deviation of 1.5 inches. Write the formula for the density function for height of five-year-old girls.

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

17) According to data from 2007, the height of five-year-old girls is normally distributed with a mean of 42 inches and a standard deviation of 1.5 inches. Use your calculator or computer to find the percentage of 5-year-old girls between 40 and 44 inches.

A) 77 B) 74 C) 12 D) 83

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

18) The density function for the shelf life, in days, of a product in a grocery store is shown in the graph.

A line is graphed on a coordinate plane. The horizontal axis labeled t ranges from 0 to 7, in increments of 1. The vertical axis is labeled p of t. The line starts at (0, 0), increases to (5, 0.286), and then decreases to (7, 0).

Estimate the median shelf life of the product.

A) 2.25 days B) 3.25 days C) 4.25 days D) 5.25 days

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the median of a density function or a cumulative distribution function.

19) A density function is given by p(t) = 0.148t((t - 3)) with superscript (2) for 0 ≤ t ≤ 3. Estimate the mean of the distribution.

A) 1.20 B) 1.54 C) 1.02 D) 1.78

Diff: 3 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the median of a density function or a cumulative distribution function.

20) A banana plant typically has about 40 leaves that emerge over a period of 238 days (8 months). Younger leaves emerge more rapidly than later leaves. If you randomly select a banana leaf, the probability density function for the month of emergence is given by p(t) = 0.294 - 0.088(1.016) with superscript (t). Use a calculator or computer to find the median time of emergence.

A) 2.7 months B) 2.4 months C) 3.3 months D) 4.0 months

Diff: 3 Var: 1

Section: 7.3

Learning Objectives: Find and interpret the median of a density function or a cumulative distribution function.

21) The race times for a group of cross-country runners are all between 15 and 25 minutes. They are represented by the density function p(t) and the corresponding cumulative distribution function P(t), where t is time in minutes. Express integral of (p(x) dx) from (15) to (20) in terms of P(t).

Diff: 1 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

22) Let p(t) = 0.2(e) with superscript (-0.2t) be the density function for call-back time by an answering service with t = time in minutes and 0 ≤ t ≤ 30. Find the mean, in minutes, to 2 decimal places.

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

23) The number of hours of sleep per night averaged by a group of students is approximately normally distributed with mean μ = 7 and standard deviation σ = 1.2. What is the probability that a student selected at random had more than 7.5 hours of sleep? Round to 2 decimal places.

Diff: 1 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

24) Which of the following distributions best describe the density function for annual popcorn sales by a Cub Scout pack if the sales are approximately normally distributed and they almost always make between $300 and $500?

A) p(x) = (1/50square root of (2π))(e) with superscript ((-(x-400)) with superscript (2)/(2(50)) with superscript (2)) B) p(x) = (1/150square root of (2π))(e) with superscript ((-(x-400)) with superscript (2)/(2(150)) with superscript (2))

C) p(x) = (1/50square root of (2π))(e) with superscript ((-(x-300)) with superscript (2)/(2(50)) with superscript (2)) D) p(x) = (1/100square root of (2π))(e) with superscript ((-(x-300)) with superscript (2)/(2(100)) with superscript (2))

Diff: 3 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.; Interpret a density function.

25) The speed of cars on a freeway are approximately normally distributed with mean μ = 78 mph and standard deviation σ = 5 mph. Assume a maximum speed of 100 mph. If speeding tickets are given to cars traveling faster than 83 mph, what is the probability that a randomly selected car is going fast enough to get a ticket? Round to 2 decimal places.

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

26) The speed of cars on a freeway are approximately normally distributed with mean μ = 78 mph and standard deviation σ = 5 mph. Assume a maximum speed of 100 mph. What percent of cars are going between 65 and 70 mph? Round to the nearest percent.

Diff: 2 Var: 1

Section: 7.3

Learning Objectives: Find probability from a normal distribution.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course. Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Document Information

Document Type:
DOCX
Chapter Number:
7
Created Date:
Aug 21, 2025
Chapter Name:
Chapter 7 Probability
Author:
Hughes Hallett

Connected Book

Final Test Bank | Applied Calculus 7e

By Hughes Hallett

Test Bank General
View Product →

$24.99

100% satisfaction guarantee

Buy Full Test Bank

Quick Navigation

Preview Document Info Connected Book Recommendations

Benefits

Immediately available after payment
Answers are available after payment
ZIP file includes all related files
Files are in Word format (DOCX)
Check the description to see the contents of each ZIP file
We do not share your information with any third party