Section 6.1 and 6.2 exercises Name - Kennesaw State University

Section 6.1 and 6.2 exercises

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the

question.

1) A normal population has a mean ¦Ì = 30 and standard deviation ¦Ò = 7. What is the

probability that a randomly chosen value will be greater than 31?

A) 0.7881

B) 0.5557

C) 0.4443

D) 0.7580

1)

2) A fast-food restaurant chain has 623 outlets in the United States. The following table

categorizes them by city population and location and presents the number of outlets in

each category. An outlet is chosen at random from the 623 to test market a new menu.

2)

Region

Population

of city

Under 50,000

50,000 - 500,000

Over 500,000

NE

30

60

72

SE

26

48

125

SW NW

27

19

50

39

79

48

Given that the outlet is located in a city with a population under 50,000, what is the

probability that it is in the Southwest?

A) 0.255

B) 0.265

C) 0.164

D) 0.043

3) Find the z-scores that bound the middle 74% of the area under the standard normal

curve.

A) -1.07, 1.07

B) -1.13, 1.13

C) -1.24, 1.24

D) -0.99, 0.99

Find the indicated probability.

4) The table below describes the smoking habits of a group of asthma sufferers.

4)

Light Heavy

Nonsmoker smoker smoker Total

Men

395

63

79

537

Women

363

86

67

516

Total

758

149

146 1053

What is the probability that a woman is a nonsmoker?

A) 0.345

B) 0.49

C) 0.720

1

D) 0.479

3)

E) 0.703

5) You are dealt a hand of three cards, one at a time. Find the probability that your cards are all

diamonds.

A) 0.231

B) 0.013

C) 0.750

D) 0.016

5)

E) 0.705

6) The table below describes the smoking habits of a group of asthma sufferers.

6)

Light Heavy

Nonsmoker smoker smoker Total

Men

331

65

61

457

Women

358

65

86

509

Total

689

130

147

966

What is the probability that a light smoker is a woman?

A) 0.135

B) 0.128

C) 0.067

D) 0.5

E) 0.713

7) An IRS auditor randomly selects 3 tax returns from 54 returns of which 10 contain errors. What is

the probability that she selects none of those containing errors?

A) 0.006

B) 0.541

C) 0.534

D) 0.005

7)

E) 0.466

8) A box contains 12 batteries of which 5 are still working. Anne starts picking batteries one at a

8)

time from the box and testing them. Find the probability that she has to pick 5 batteries in order

to find one that works.

A) 6.031

B) 0.013

C) 0.017

D) 0.044

E) 0.001

9) You are dealt a hand of three cards, one at a time. Find the probability that your third card is your

first ace.

A) 0.127

B) 0.00018

C) 0.068

D) 0.077

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

A) 0.1210

B) 0.2420

C) 0.7580

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

A) 0.0548

B) 0.0274

C) 0.9452

E) 0.145

10)

D) 0.2580

11)

D) 0.4452

12) The mean number of pets per household is 3.25 with standard deviation 1.3. A sample

of 59 households is drawn. Find the 74th percentile of the sample mean.

A) 3.36

B) 2.70

C) 3.86

D) 4.11

Solve the problem. Round to the nearest tenth.

13) For a recent English exam, use the Normal model N(73, 9.2) to find the score that represents the

90th percentile.

A) 84.8

B) 63.8

C) 61.2

D) 82.2

E) 81.3

2

9)

12)

13)

14) For a recent English exam, use the Normal model N(73, 9.2) to find the score that represents the

30th percentile.

A) 61.2

B) 63.8

C) 82.2

D) 77.8

14)

E) 68.2

15) Based on the Normal model for car speeds on an old town highway N(77, 9.1), what is the cutoff

15)

value for the highest 15% of the speeds?

A) about 63.1 mph

B) about 65.5 mph

C) about 11.6 mph

D) about 67.5 mph

E) about 86.5 mph

16) A fast-food restaurant chain has 617 outlets in the United States. The following table

categorizes them by city population and location and presents the number of outlets in

each category. An outlet is chosen at random from the 617 to test market a new menu.

16)

Region

Population

of city

Under 50,000

50,000 - 500,000

Over 500,000

NE

32

50

76

SE

32

41

125

SW NW

26

16

56

40

78

45

Given that the outlet is located in the West (either SW or NW), what is the probability th

it

is in a city with population 50,000¨C500,000?

A) 0.156

B) 0.368

C) 0.268

D) 0.716

Solve the problem.

17) A bank?s loan officer rates applicants for credit. The ratings can be described by a Normal model

with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, what

percentage can be expected to be between 200 and 275?

A) 43.32%

B) 5.00%

C) 6.68%

D) 93.32%

E) 42.37%

18) For a recent English exam, use the Normal model N(73, 9.2) to find the percent of scores over 85.

Round to the nearest tenth of a percent.

A) 9.7%

B) 11.5%

C) 88.5%

D) 8.1%

18)

E) 90.3%

19) The lengths of human pregnancies can be described by a Normal model with a mean of 268 days

and a standard deviation of 15 days. What percentage can we expect for a pregnancy that will last

at least 300 days?

A) 98.34%

B) 1.79%

C) 1.66%

D) 1.99%

E) 48.34%

3

17)

19)

20) The volumes of soda in quart soda bottles can be described by a Normal model with a mean of

20)

32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a

volume less than 32 oz?

A) 9.87%

B) 40.13%

C) 47.15%

D) 59.87%

E) 38.21%

21) A town?s average snowfall is 46 inches per year with a standard deviation of 10 inches. Using a

21)

Normal model, what values should border the middle 68% of the model?

A) 48 inches and 44 inches

B) 66 inches and 26 inches

C) 46 inches and 42.6 inches

D) 56 inches and 36 inches

E) 51 inches and 41 inches

22) The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a

mean 8.6 pounds and standard deviation 1.9 pounds. A turkey farmer wants to provide

a money-back guarantee that her 6-week poults will weigh at least a certain amount.

What weight should she guarantee so that she will have to give her customer's money

back only 1% of the time?

A) 4.17 lb

B) 5.00 lb

C) 3.34 lb

D) 4.59 lb

22)

23) A normal population has a mean ¦Ì = 34 and standard deviation ¦Ò = 11. What proportion

of the population is less than 41?

A) 0.2611

B) 1.0000

C) 0.7389

D) 0.8106

23)

24) A normal population has a mean ¦Ì = 27 and standard deviation ¦Ò = 9. What proportion

of the population is between 26 and 31?

A) 0.6700

B) 0.2138

C) 0.4562

D) 0.7862

24)

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

A) 1.59

B) 1.48

C) 1.35

25)

D) 1.74

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. What

proportion of bottles have volumes less than 995 mL?

A) 0.5793

B) 0.9974

C) 0.5596

D) 1.0000

26)

27) A normal population has a mean ¦Ì = 10 and standard deviation ¦Ò = 2. What is the 86th

percentile of the population?

A) 13.38

B) 12.16

C) 10.94

D) 9.73

27)

4

28) A sample of size 40 will be drawn from a population with mean 98 and standard

deviation 24. Find the 21st percentile of x.

A) 93.8

B) 90.8

C) 94.9

D) 91.4

28)

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

A) 0.4772

B) 0.0132

C) 0.5228

D) 0.9868

29)

30) The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and the

slips are placed into a hat. If the slips are drawn randomly without replacement, what is

the probability that "A" is drawn first and "B" is drawn second?

A) 0.033

B) 0.039

C) 0.024

D) 0.028

30)

31) A sample of size 42 will be drawn from a population with mean 34 and standard

deviation 8. Find the probability that x will be greater than 36.

A) 0.0351

B) 0.0749

C) 0.0526

D) 0.9474

31)

32) A certain car model has a mean gas mileage of 29 miles per gallon (mpg) with a

standard deviation 5 mpg. A pizza delivery company buys 38 of these cars. What is the

probability that the average mileage of the fleet is greater than 27.8 mpg?

A) 0.9535

B) 0.8599

C) 0.0465

D) 0.9306

32)

33) The mean annual income for people in a certain city (in thousands of dollars) is 38,

with a standard deviation of 31. A pollster draws a sample of 43 people to interview.

Find the 68th percentile of the sample mean.

A) 40.2 thousand dollars

B) 37.7 thousand dollars

C) 38.7 thousand dollars

D) 42.3 thousand dollars

33)

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