Deck 7: Confidence Intervals

Question 1

Find the shaded area under the standard normal curve. )

A)0.8944
B)0.1056
C)0.3944
D)0.0528

Answer 1

B

Question 2

Find the z-scores that bound the middle 74% of the area under the standard normal curve.

A)-1.13, 1.13
B)-1.24, 1.24
C)-0.99, 0.99
D)-1.07, 1.07

Answer 2

A

Question 3

Find

A) 1.44
B) 1.34
C) 1.08
D) 1.51

Answer 3

1.44

Question 4

The following figure is a probability density curve that represents the lifetime,) Find the proportion of batteries with lifetimes less than 20 months.

A)0.24
B)0.25
C)0.75
D)0.49

Question 5

Find the shaded area under the standard normal curve. )

A)0.5122
B)0.9878
C)0.4878
D)0.2439

Question 6

A normal population has a mean and standard deviation What is the 86 th percentile of the population?

A) 10.94
B) 9.73
C) 13.38
D) 12.16

Question 7

The following figure is a probability density curve that represents the lifetime, in months, of a Find the proportion of batteries with lifetimes between 10 and 20 months.

A)0.74
B)0.06
C)0.26
D)0.20

Question 8

Find the area under the standard normal curve that lies outside the interval betweenz = -2.2 and z = -1.3.

A)0.4032
B)0.9171
C)0.0829
D)0.5968

Question 9

Find the area under the standard normal curve to the left of z = -0.7.

A)0.7580
B)0.2580
C)0.1210
D)0.2420

Question 10

Find the z-score for which the area to the left is 0.79.

A)1.04
B)0.58
C)0.64
D)0.81

Question 11

Find the z-score for which the area to the right is 0.07.

A)1.59
B)1.35
C)1.48
D)1.74

Question 12

Find the area under the standard normal curve to the right of z = 1.6.

A)0.0548
B)0.4452
C)0.0274
D)0.9452

Question 13

A normal population has a mean and standard deviation What proportion of the population is between 26 and 31 ?

A) 0.2138
B) 0.7862
C) 0.4562
D) 0.6700

Question 14

Find the shaded area under the standard normal curve. )

A)0.0528
B)0.3944
C)0.1056
D)0.8944

Question 15

A normal population has a mean and standard deviation What proportion of the population is less than 41 ?

A) 0.8106
B) 1.0000
C) 0.2611
D) 0.7389

Question 16

The following figure is a probability density curve that represents the lifetime,) What is the probability that a randomly chosen battery lasts longer than 20 months?

A)0.49
B)0.24
C)0.25
D)0.51

Question 17

Find the area under the standard normal curve that lies between z = 1.8 and z = 2.

A)0.0132
B)0.4772
C)0.5228
D)0.9868

Question 18

A normal population has a mean and standard deviation What is the probability that a randomly chosen value will be greater than 31 ?

A) 0.4443
B) 0.7881
C) 0.5557
D) 0.7580

Question 19

A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters(mL)and standard deviation 4 mL. The fill volumes are normally distributed. Whatproportion of bottles have volumes greater than 994 mL?

A)1.0000
B)0.8944
C)0.9599
D)0.8925

Question 20

Find the shaded area under the standard normal curve. )

A)0.4878
B)0.8291
C)0.1709
D)0.0854

Question 21

The weights of 6-week-old poults (juvenile turkeys)are normally distributed with a mean9.1 pounds and standard deviation 2.4 pound(s). Find the 13th percentile of the weights.

A)7.67 lb
B)6.39 lb
C)7.03 lb
D)5.75 lb

Question 22

The weights of 6-week-old poults (juvenile turkeys)are normally distributed with a mean9.1 pounds and standard deviation 2.4 pounds. Find the first quartile of the weight.

A)8.24 lb
B)8.99 lb
C)6.74 lb
D)7.49 lb

Question 23

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is , and the sample proportion is

A) 0.9463
B) 0.9525
C) 0.9306
D) 0.9474

Question 24

The mean annual income for people in a certain city (in thousands of dollars)is 38, witha standard deviation of 31. A pollster draws a sample of 43 people to interview. Find the68th percentile of the sample mean.

A)37.7 thousand dollars
B)38.7 thousand dollars
C)40.2 thousand dollars
D)42.3 thousand dollars

Question 25

For a particular diamond mine, 76% of the diamonds fail to qualify as "gemstone grade". A random sample of 96 diamonds is analysed. Find the mean

A) 0.044
B) 0.24
C) 0.96
D) 0.76

Question 26

A bottler of drinking water fills plastic bottles with a mean volume of 994 milliliters(mL)and standard deviation 5 mL. The fill volumes are normally distributed. Whatproportion of bottles have volumes less than 995 mL?

A)0.5793
B)0.9974
C)0.5596
D)1.0000

Question 27

The mean annual income for people in a certain city (in thousands of dollars)is 40, witha standard deviation of 35. A pollster draws a sample of 48 people to interview. What isthe probability that the sample mean income is between 34 and45 (thousands of dollars)?

A)0.2781
B)0.1611
C)0.8389
D)0.7219

Question 28

A sample of size 39 will be drawn from a population with mean 26 and standard deviation 14. Find the probability that will be less than 29 .

A) 0.8925
B) 0.0901
C) 0.9099
D) 0.8770

Question 29

A sample of size 70 will be drawn from a population with mean 24 and standard deviation 10. Find the probability that will be between 22 and 25 .

A) 0.7521
B) 0.0475
C) 0.7326
D) 0.2005

Question 30

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is , and the sample proportion is

A) 0.0749
B) 0.1251
C) 0.9251
D) 0.8000

Question 31

A ferry will safely accommodate 66 tons of passenger cars. Assume that the mean weightof a passenger car is 1.7 tons with standard deviation 0.5 tons. If a random sample of 36cars are loaded onto the ferry, what is the probability that the maximum safe weight willbe exceeded?

A)0.0548
B)0.0668
C)0.9452
D)0.0384

Question 32

A bottler of drinking water fills plastic bottles with a mean volume of 993 milliliters(mL)and standard deviation 6 mL. The fill volumes are normally distributed. Whatproportion of bottles have volumes between 991 mL and 997 mL?

A)0.3779
B)0.7486
C)0.3707
D)0.3377

Question 33

A certain car model has a mean gas mileage of 29 miles per gallon (mpg)with a standarddeviation 5 mpg. A pizza delivery company buys 38 of these cars. What is the probabilitythat the average mileage of the fleet is greater than 27.8 mpg?

A)0.9535
B)0.9306
C)0.0465
D)0.8599

Question 34

Use the Central Limit Theorem to find the indicated probability. The sample size is n , the population proportion is , and the sample proportion is

A) 0.6103
B) 0.3483
C) 0.3300
D) 0.3897

Question 35

A sample of size 42 will be drawn from a population with mean 34 and standard deviation 8. Find the probability that will be greater than 36 .

A) 0.0526
B) 0.9474
C) 0.0749
D) 0.0351

Question 36

A sample of size 40 will be drawn from a population with mean 98 and standard deviation 24. Find the 21st percentile of

A) 90.8
B) 91.4
C) 93.8
D) 94.9

Question 37

The mean number of pets per household is 3.25 with standard deviation 1.3. A sample of59 households is drawn. Find the 74th percentile of the sample mean.

A)4.11
B)2.70
C)3.86
D)3.36

Question 38

The weights of 6-week-old poults (juvenile turkeys)are normally distributed with a mean8.6 pounds and standard deviation 1.9 pounds. A turkey farmer wants to provide amoney-back guarantee that her 6-week poults will weigh at least a certain amount. Whatweight should she guarantee so that she will have to give her customer's money backonly 1% of the time?

A)4.59 lb
B)3.34 lb
C)5.00 lb
D)4.17 lb

Question 39

The mean annual income for people in a certain city (in thousands of dollars)is 42, witha standard deviation of 38. A pollster draws a sample of 40 people to interview. What isthe probability that the sample mean income is less than 35 (thousands of dollars)?

A)0.8554
B)0.1210
C)0.1446
D)0.0934

Question 40

A certain car model has a mean gas mileage of 31 miles per gallon (mpg)with a standarddeviation 3 mpg. A pizza delivery company buys 35 of these cars. What is the probabilitythat the average mileage of the fleet is between 30.9 and 31.2 mpg?

A)0.2310
B)0.6517
C)0.4207
D)0.7690

Question 41

Use the normal approximation to find the indicated probability. The sample size is n , the population proportion of successes is p , and X is the number of successes in the sample.

A) 0.3936
B) 0.3446
C) 0.6406
D) 0.3594

Question 42

At a cell phone assembly plant, 77% of the cell phone keypads pass inspection. Arandom sample of 111 keypads is analysed. Find the probability that the proportion of thesample keypads that pass inspection is between 0.72 and 0.8.

A)0.6677
B)0.8944
C)0.1056
D)0.7734

Question 43

At a cell phone assembly plant, 81% of the cell phone keypads pass inspection. Arandom sample of 97 keypads is analysed. Find the probability that more than 85% of thesample keypads pass inspection.

A)0.1587
B)0.8413
C)0.8577
D)0.1423

Question 44

At a cell phone assembly plant, 77% of the cell phone keypads pass inspection. A random sample of 98 keypads is analysed. Find the mean

A) 0.23
B) 0.77
C) 0.96
D) 0.043

Question 45

A gardener buys a package of seeds. Seventy-five percent of seeds of this type germinate.The gardener plants 90 seeds. Approximate the probability that the number of seeds thatgerminate is between 57.5 and 72.5 exclusive.

A)0.1461
B)0.8643
C)0.8539
D)0.0104

Question 46

A gardener buys a package of seeds. Eighty-two percent of seeds of this type germinate.The gardener plants 130 seeds. Approximate the probability that 99 or more seedsgerminate.

A)0.9803
B)0.9678
C)0.9884
D)0.9842

Question 47

Use the normal approximation to find the indicated probability. The sample size is n , the population proportion of successes is p , and X is the number of successes in the sample.

A) 0.6330
B) 0.1251
C) 0.7580
D) 0.2420

Question 48

A gardener buys a package of seeds. Eighty-five percent of seeds of this type germinate.The gardener plants 110 seeds. Approximate the probability that fewer than 85 seedsgerminate.

A)0.0082
B)0.9918
C)0.9964
D)0.0036

Question 49

For a particular diamond mine, 77% of the diamonds fail to qualify as "gemstone grade".A random sample of 112 diamonds is analysed. Find the probability that more than 81%of the sample diamonds fail to qualify as gemstone grade.

A)0.8729
B)0.1271
C)0.1562
D)0.8438

Question 50

Use the normal approximation to find the indicated probability. The sample size is n , the population proportion of successes is p , and X is the number of successes in the sample.

A) 0.1210
B) 0.8888
C) 0.8621
D) 0.8790

Question 51

For a particular diamond mine, 75% of the diamonds fail to qualify as "gemstone grade".A random sample of 110 diamonds is analysed. Find the probability that less than 81%of the sample diamonds fail to qualify as gemstone grade.

A)0.0735
B)0.9265
C)0.0548
D)0.9452

Question 52

A public relations firm found that only 88% of voters in a certain state are satisfied with their state representative. How large a sample of voters should be drawn so that the sample proportion of voters who are satisfied with their representative is approximately normally distributed?

A) 101
B) 12
C) 84
D) 10

Question 53

Use the normal approximation to find the indicated probability. The sample size is n , the population proportion of successes is p , and X is the number of successes in the sample.

A) 0.6179
B) 0.0375
C) 0.5804
D) 0.3821

Question 54

For a particular diamond mine, 80% of the diamonds fail to qualify as "gemstone grade". A random sample of 113 diamonds is analysed. Find the mean

A) 0.20
B) 0.96
C) 0.80
D) 0.038

Question 55

At a cell phone assembly plant, 83% of the cell phone keypads pass inspection. Arandom sample of 192 keypads is analysed. Find the probability that less than 86% of thesample keypads pass inspection.

A)0.8962
B)0.1335
C)0.8665
D)0.1038

Question 56

Use the normal approximation to find the indicated probability. The sample size is n , the population proportion of successes is , and X is the number of successes in the sample.
ppp

A) 0.7611
B) 0.2743
C) 0.7517
D) 0.7257

Question 57

For a particular diamond mine, 82% of the diamonds fail to qualify as "gemstone grade".A random sample of 90 diamonds is analysed. Find the probability that the proportion ofthe sample diamonds that fail to qualify as gemstone grade is between 0.78 and 0.88.

A)0.7695
B)0.1611
C)0.9306
D)0.8389

Question 58

Use the normal approximation to find the indicated probability. The sample size is n , the population proportion of successes is p , and X is the number of successes in the sample.

A) 0.1423
B) 0.1611
C) 0.1292
D) 0.8708

Question 59

A public relations firm found that only 9 % of voters in a certain state are satisfied with their U.S. senators. How large a sample of voters should be drawn so that the sample proportion of voters who are satisfied with their senators is approximately normally distributed?

A) 11
B) 10
C) 125
D) 112

Question 60

At a cell phone assembly plant, 80 % of the cell phone keypads pass inspection. A random sample of 116 keypads is analysed. Find the mean

A) 0.80
B) 0.20
C) 0.037
D) 0.96

Question 61

The following stem-and-leaf plots each illustrate a sample. )

Question 62

The following boxplots each illustrate a sample. )

Question 63

The following dotplots each illustrate a sample. )

Question 64

Airlines often sell more tickets for a flight than there are seats because some ticketholders do not show up for the flight. Assume that an airplane has 170 seats forpassengers and that the probability that a person holding a ticket appears for the flight is0.93. If the airline sells 176 tickets, what is the probability that everyone who appears forthe flight will get a seat?

A)0.9625
B)0.9515
C)0.9778
D)0.9608

Question 65

The following histograms each illustrate a sample. )