Deck 5: Approximating With a Distribution

Question 1

Use the following
Select the answer closest to the specified areas for a N(0, 1) density.

-The area to the left of z = -1.52

A) 0.064
B) 0.106
C) 0.936
D) 0.147

Answer 1

0.064

Question 2

Use the following
Select the answer closest to the specified areas for a N(0, 1) density.

-The area to the right of z = -0.47

A) 0.341
B) 0.77
C) 0.681
D) 0.319

Answer 2

0.681

Question 3

Use the following
Select the answer closest to the specified areas for a N(0, 1) density.

-The area between z = 0.51 and z = 2.79.

A) 0.695
B) 0.302
C) 0.692
D) 0.997

Answer 3

0.302

Question 4

Use the following
Select the answer closest to the specified areas for a N(0, 1) density.

-The area outside of the interval z = -2.13 and z = 1.11.

A) 0.133
B) 0.017
C) 0.85
D) 0.15

Question 5

Use the following
Find the endpoint(s) on a N(0, 1) density with the given property.

-The area to the left of the endpoint is about 0.2.

A) -2.054
B) 0.842
C) -0.842
D) 2.054

Question 6

Use the following
Find the endpoint(s) on a N(0, 1) density with the given property.

-The area to the right of the endpoint is about 0.45.

A) 0.126
B) 1.695
C) -1.695
D) -0.126

Question 7

Use the following
Find the endpoint(s) on a N(0, 1) density with the given property.

-The area between $\pm z$ is about 0.99

A) 2.326
B) 2.225
C) 2.125
D) 2.575

Question 8

Use the following
Select the answer closest to the specified areas for a normal density.

-The area to the left of 32 on a N(45, 8) distribution.

A) 0.948
B) 0.052
C) 0.896
D) 0.104

Question 9

Use the following
Select the answer closest to the specified areas for a normal density.

-The area to the right of 12 on a N(9.4, 1.2) distribution.

A) 0.985
B) 0.97
C) 0.03
D) 0.015

Question 10

Use the following
Select the answer closest to the specified areas for a normal density.

-The area between 43 and 100 on a N(75, 15) distribution.

A) 0.984
B) 0.952
C) 0.936
D) 0.64

Question 11

Use the following
Find the endpoint(s) on the normal density curve with the given property.

-The area to the left of the endpoint on a N(25, 3) curve is about 0.1.

A) 21.155
B) 28.845
C) 31.978
D) 18.022

Question 12

Use the following
Find the endpoint(s) on the normal density curve with the given property.

-The area to the right of the endpoint on a N(100, 17) curve is about 0.05.

A) 72.037
B) 100
C) 143.783
D) 127.963

Question 13

Use the following
Find the endpoint(s) on the normal density curve with the given property.

-The symmetric middle area on a N(66, 6) curve is about 0.9.

A) 54.241 and 77.759
B) 56.131 and 75.869
C) 61.953 and 70.047
D) 59.098 and 72.902

Question 14

Use the following
It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university.
-Draw a sketch of the distribution of men's heights and label at least three points on the horizontal axis.

Question 15

Use the following
It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university.
-The beds that the university currently purchases are 75 inches long. What proportion of males will be able to fit on the bed while lying perfectly straight? Round your answer to three decimal places.

Question 16

Use the following
It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university.
-Should the university be concerned that females will not fit in the 75 inch beds? Numerically justify your answer.

Question 17

Use the following
It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university.
-The university plans on ordering custom sized beds such that 99% of male students are expect to fit in them when lying perfectly straight. What length beds should they order? Round your answer to the nearest inch.

Question 18

Use the following
It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches and that the heights of adult females in the U.S. are also approximately normally distributed with mean 64 inches (5 feet, 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering beds for their dorm rooms. Answer the following questions about the lengths of beds in dorm rooms at this university.
-The university decides it is too expensive to replace all the beds. Suppose the university has 2,150 beds all of which are 75 inches long. How many beds should they replace? You may assume that only those males taller than 75 inches will receive the longer beds and that females make up half of the population that will need a dorm room bed.

Question 19

Use the following
In the following, convert an area from one normal distribution to an equivalent area for a different normal distribution. Show details of your calculation. Draw sketches of both normal distributions, find and label the endpoints, and shade the regions on both curves.
-The area to the left of 16 for a N(20, 3) distribution converted to a standard normal distribution

Question 20

Use the following
In the following, convert an area from one normal distribution to an equivalent area for a different normal distribution. Show details of your calculation. Draw sketches of both normal distributions, find and label the endpoints, and shade the regions on both curves.
-The "Q1" for a standard normal distribution converted to a N(15, 2.5) distribution.

Question 21

Use the following
In the following, convert an area from one normal distribution to an equivalent area for a different normal distribution. Show details of your calculation. Draw sketches of both normal distributions, find and label the endpoints, and shade the regions on both curves.
-The area to the right of 50 in a N(40, 8) distribution converted to a standard normal distribution.

Question 22

Use the following
In the following, convert an area from one normal distribution to an equivalent area for a different normal distribution. Show details of your calculation. Draw sketches of both normal distributions, find and label the endpoints, and shade the regions on both curves.
-The middle 90% for a standard normal distribution converted to a N(45, 15) distribution.

Question 23

Use the following
Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 inches.

-Draw a sketch of this normal distribution and label at least three points on the horizontal axis.

Question 24

Use the following
Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 inches.
-What proportion of 10-year-old girls are shorter than 48 inches (4 feet)? Report your answer with four decimal places.

Question 25

Use the following
Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 inches.
-What proportion of 10-year-old girls are taller than 60 inches (5 feet)? Report your answer with three decimal places.

Question 26

Use the following
Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 inches.
-What proportion of 10-year-old girls have heights between 50 and 55 inches? Report your answer with three decimal places.

Question 27

Use the following
Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 inches.
-A parent says her 10-year-old daughter is in the 95th percentile in height. How tall is the girl? Report your answer with one decimal place.

Question 28

Use the following
Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 inches.
-The tallest 15% of 10-year-old girls are taller than what height? Report your answer with one decimal place.

Question 29

Use the following
Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 inches.
-What is the first quartile of heights of 10-year-old girls? Report your answer with one decimal place.

Question 30

Use the following
Heights of 10-year-old girls (5th graders) follow an approximately normal distribution with mean = 54.4 inches and standard deviation of = 2.7 inches.
-What is the IQR of heights of 10-year-old girls? Note that you will need to find two endpoints of the distribution for your calculation. Report you answer with one decimal place.

Question 31

Use the following
Use the provided density function to choose the best estimate for the proportion of the population found in the specified region.


-The percent of the population that is less than 20 is closest to

A) 5%
B) 25%
C) 75%
D) 95%

Question 32

Use the following
Use the provided density function to choose the best estimate for the proportion of the population found in the specified region.


-The percent of the population that is less than 40 is closest to

A) 15%
B) 35%
C) 75%
D) 95%

Question 33

Use the following
Use the provided density function to choose the best estimate for the proportion of the population found in the specified region.


-The percent of the population that is more than 100 is closest to

A) 75%
B) 20%
C) 10%
D) 2%

Question 34

Use the following
Use the provided density function to choose the best estimate for the proportion of the population found in the specified region.


-The percent of the population that is more than 50 is closest to

A) 25%
B) 75%
C) 50%
D) 90%

Question 35

Use the following
Use the provided density function to choose the best estimate for the proportion of the population found in the specified region.


-The percent of the population between 20 and 80 is closest to

A) 85%
B) 99%
C) 70%
D) 50%

Question 36

Use the following
A student suspects that the length of songs currently on his iPod are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds.
-Draw a sketch of this normal distribution and label at least three points on the horizontal axis.

Question 37

Use the following
A student suspects that the length of songs currently on his iPod are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds.
-What proportion of songs are less than 180 seconds (3 minutes)? Report your answer with three decimal places.

Question 38

Use the following
A student suspects that the length of songs currently on his iPod are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds.
-What proportion of songs are longer than 300 seconds (5 minutes)? Report your answer with three decimal places.

Question 39

Use the following
A student suspects that the length of songs currently on his iPod are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds.
-What proportion of songs are between 240 and 360 seconds (4 minutes and 6 minutes)? Report your answer with three decimal places.

Question 40

Use the following
A student suspects that the length of songs currently on his iPod are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds.
-The shortest 10% of songs are shorter than what length? Report your answer with one decimal place.

Question 41

Use the following
A student suspects that the length of songs currently on his iPod are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds.
-The longest 25% of songs are longer than what length? Report your answer with one decimal place.

Question 42

Use the following
A student suspects that the length of songs currently on his iPod are approximately normally distributed with a mean of 257 seconds and standard deviation 62 seconds.
-The symmetric middle 90% of songs have lengths between what two values? Round all values to one decimal place.

Question 43

Use the following
Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-Draw a sketch of this normal distribution and label at least three points on the horizontal axis.

Question 44

Use the following
Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-What proportion of robins have wingspans less than 13 inches? Report your answer with three decimal places.

Question 45

Use the following
Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-What proportion of robins have wingspans longer 15.5 inches? Report your answer with three decimal places.

Question 46

Use the following
Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-What proportion of robins have wingspans between 12.5 and 13.5 inches? Report your answer with three decimal places.

Question 47

Use the following
Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-What is the 30th percentile of robin wingspans? Report your answer with two decimal places.

Question 48

Use the following
Robins are common birds in North America. Suppose that the wingspan of robins is approximately normal with mean 14 inches and standard deviation 0.7 inches.
-The largest 20% of robins have wingspans longer than what value? Report your answer with two decimal places.

Question 49

Use the following
Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-Draw a sketch of this normal distribution and label at least three points on the horizontal axis.

Question 50

Use the following
Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-In Professor Albert's course, students who earn less than a 60% in the class are assigned a failing grade (F). What proportion of the students earned F's? Report your answer with three decimal places.

Question 51

Use the following
Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-In Professor Albert's course, students who earn above a 94% are assigned an "A". What proportion of students earned A's? Report your answer with three decimal places.

Question 52

Use the following
Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-What proportion of students earn between an 82% and 88% in this class? Report your answer with three decimal places.

Question 53

Use the following
Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-What is the 25th percentile in this course? Report your answer with one decimal place.

Question 54

Use the following
Final grades in Professor Albert's large calculus class are approximately normally distributed with a mean of 76 (%) and standard deviation of 8 (%).
-The top 30% of students earned scores above what value? Report your answer with one decimal place.

Question 55

Use the following
Find the z* values based on a standard normal distribution for each of the following.

-An 86% confidence interval for a proportion

A) 1.080
B) 1.476
C) 0.994
D) 1.96

Question 56

Use the following
Find the z* values based on a standard normal distribution for each of the following.

-An 88% confidence interval for a correlation.

A) 2.575
B) 1.175
C) 2.326
D) 1.555

Question 57

Use the following
Find the z* values based on a standard normal distribution for each of the following.

-A 78% confidence interval for a mean.

A) 0.772
B) 1.227
C) 1.514
D) 1.126

Question 58

Use the following
Find the z* values based on a standard normal distribution for each of the following.

-A 66% confidence interval for a slope.

A) 0.954
B) 0.412
C) 0.754
D) 1.016

Question 59

Use the following
A set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution are provided. Find the value of the standardized z-test statistic.

-Test H_o: p = 0.75 versus H_a: p > 0.75 when the sample has n = 20, = 0.78, and SE = 0.015.

A) 0.03
B) 2
C) -2
D) 1.5

Question 60

Use the following
A set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution are provided. Find the value of the standardized z-test statistic.

-Test versus when the sample has n = 75, = 25.5, s = 5.4, and SE = 0.6.

A) -1.5
B) 0.278
C) 2.5
D) -0.833

Question 61

Use the following
A set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution are provided. Find the value of the standardized z-test statistic.

-Test and when the samples have n₁ = 35, = 78, s₁ = 15, n₂ = 40, = 72, and s₂ = 12. The standard error of from the randomization distribution is 3.2.

A) 1.875
B) 6
C) 0.4
D) 0.5

Question 62

Use the following
Find the p-value based on a standard normal distribution for the standardized test statistic and provided alternative hypothesis.

-z = -1.86 for

A) 0.031
B) 0.969
C) 0.062
D) 0.937

Question 63

Use the following
Find the p-value based on a standard normal distribution for the standardized test statistic and provided alternative hypothesis.

-z = 2.36 for

A) 0.982
B) 0.0182
C) 0.991
D) 0.0091

Question 64

Use the following
Find the p-value based on a standard normal distribution for the standardized test statistic and provided alternative hypothesis.

-z = 1.75 for

A) 0.960
B) 0.040
C) 0.080
D) 0.920

Question 65

Use the following
In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. The bootstrap distribution (based on 5,000 samples) is provided.

-Would it be appropriate to use the normal distribution to construct the confidence interval in this situation? Explain briefly.

Question 66

Use the following
In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. The bootstrap distribution (based on 5,000 samples) is provided.

-The standard error from the bootstrap distribution is SE = 0.016. Use the normal distribution to construct and interpret a 99% confidence interval for the proportion of U.S. adults who are dissatisfied with the education students receive in kindergarten through grade 12. Round to three decimal places.

Question 67

In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. Use the normal distribution to test if the proportion of U.S. adults who are dissatisfied with the education that students receive in kindergarten through grade 12 differs from 50%. The randomization distribution for this test is approximately normal and the standard error is SE = 0.016. Include all details of the test and use a 5% significance level.

Question 68

A sample of 148 college students reports sleeping an average of 6.85 hours on weeknights. The sample size is large enough to use the normal distribution, and a bootstrap distribution shows that the standard error is SE = 0.175. Use a normal distribution to construct and interpret a 95% confidence interval for the mean amount of weeknight sleep students get at this university. Use two decimal places in your answer.

Question 69

On November 15 - 18, 2012 Gallup conducted a survey of 1,015 randomly selected U.S. adults about "Black Friday"
shopping. They asked the following question:
"As you know, the Friday after Thanksgiving is one of the biggest shopping days of the year.
Looking ahead, do you personally plan on shopping on the Friday after Thanksgiving, or not?"
Of the 515 men who responded, 16% said "Yes."
Of the 500 women who responded, 20% said "Yes."The standard error of the differences in proportions ( ) is about SE = 0.025. Use the normal distribution to test, at the 5% level, if the proportions of men and women who planned to shop on the Friday after Thanksgiving are significantly different. The sample size is large enough to use the normal distribution.

Question 70

Use the following
The gas prices for a random sample of n = 10 gas stations in the state of Illinois on August 8, 2012 have a mean $3.975, with standard deviation $0.2266.
-The bootstrap distribution, based on 5,000 samples, is provided. Would it be appropriate to use the normal distribution to construct a confidence interval for the mean gas price in Illinois on August 8, 2012? Explain briefly.

Question 71

Use the following
The gas prices for a random sample of n = 10 gas stations in the state of Illinois on August 8, 2012 have a mean $3.975, with standard deviation $0.2266.
-The standard error from the bootstrap distribution is SE = 0.069. Use the normal distribution to construct and interpret a 90% confidence interval for the mean gas price in Illinois (on August 8, 2012). Round all values to two decimal places.

Question 72

Use the following
There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. The n_m = 13 male students watched an average of 6 hours of television per week with standard deviation 4.24 hours. The n_f = 11 female students watched an average of 3.91 hours of televion per week with a standard deviation of 3.48 hours. Assume that the students enrolled in the statistics class are representative of all students at the university.
-The randomization distribution for (where and are the sample mean amount of television watched by male and female students, respectively) is provided. Would it be appropriate to use the normal distribution to perform a test comparing the mean amount of television watched per week by male and female students at this university? Explain briefly.

Question 73

Use the following
There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. The n_m = 13 male students watched an average of 6 hours of television per week with standard deviation 4.24 hours. The n_f = 11 female students watched an average of 3.91 hours of televion per week with a standard deviation of 3.48 hours. Assume that the students enrolled in the statistics class are representative of all students at the university.
-The standard error of the differences is about SE = 1.667. Use the normal distribution to test, at the 5% level, if male students at this university watch, on average, more television than female students. Include all details of the test.

Question 74

A biologist interested in estimating the correlation between the body mass (in grams) and body length (in cm) of porcupines has a random sample of 18 porcupines with r = 0.407. The bootstrap distribution she constructed is approximately normal and the standard error is estimated to be 0.165. Use the normal distribution to construct and interpret a 98% confidence interval for the correlation between body mass and body length in porcupines. Round all values to three decimal places.