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A P P E N D I X C

Probability and Probability Distributions

Retirement Contributions

17. Use a graphing utility to construct a probability distribution

12.

The employees of a com-

for the percentages of profit. Use intervals of width 0.5,

pany contribute 7% of their biweekly salary to a company-

starting with the interval

14.0 < x ≤ 14.5.

sponsored retirement plan. The contributed amounts (in

dollars) for the company’s 35 employees are as follows.

18. Use a graphing utility to construct a probability distribution

for the percentages of profit. Use intervals of width 1.0,

100 200 130 136 161 156 209

starting with the interval

14.0 < x ≤ 15.0.

126 135

98 114 117 168 133

140 124 172 127 143 157 124

19. Use a graphing utility or spreadsheet software program to

152 104 126 155

92 194 115

construct a probability distribution for the following fre-

120 136 148 112 116 146

96

quency distribution.

(a) Construct a frequency distribution using groups of 20,

with the first group

90 < x ≤ 110.

Random variable, x

1

2

3

4

5

6

(b) Construct a histogram for the frequency distribution.

2

4

6

6

4

2

Frequency of x, n x

Basketball Scores

13.

A basketball team’s scores during

the playing season are as follows.

20. Use a graphing utility or spreadsheet software program

54 68 50 65 61 72 58 55 46 69

to construct a probability distribution for the following

60 52 62 56 78 74 53 58 57 71

frequency distribution.

76 54 56 62 49 60 58 70 64 45

(a) Construct a frequency distribution using groups of five,

Random variable, x

2

3

4

5

6

7

with the first group

45 ≤ x < 50.

Frequency of x, n x

2

4

6

8

10

12

(b) Construct a histogram for the frequency distribution.

Qualifying Times

14.

The qualifying times for a sports

Random variable, x

8

9

10

11

12

event are as follows.

Frequency of x, n x

10

8

6

4

2

1.14 1.54 1.22 2.00 2.06

1.30 1.24 1.19 1.34 2.01

1.15 1.13 1.15 1.47 1.20

In Exercises 21–24, use a graphing utility to construct a

1.26 1.07 2.16 1.41 1.42

probability distribution for the experiment.

(a) Construct a frequency distribution using intervals of

21. Three cards are drawn (without replacement) from a stan-

width 0.2, starting with the interval

1.00 ≤ x < 1.20.

dard deck of 52 playing cards, and the number of face cards

(b) Construct a histogram for the frequency distribution.

is counted.

Dice

15.

Two four-sided dice are tossed. Sketch the graph of

22. Three cards are drawn (without replacement) from a stan-

the probability distribution for the random variable

dard deck of 52 playing cards, and the number of kings is

giving the sum of the points on the two dice.

counted.

Dice

16.

Three four-sided dice are tossed. Sketch the graph

23. A baseball player with a batting average of 0.330 comes

of the probability distribution for the random variable

to bat three times in a game, and the number of hits is

giving the sum of the points on the three dice.

counted.

24. Three dice are tossed and the number of 5’s is counted.

Profit

In Exercises 17 and 18, use the following data,

which show the percentages of profit for a medical

supply company for the years 1993 through 2008.

Year

Profit

Year

Profit

1993

15.9%

2001

15.6%

1994

14.9%

2002

14.9%

1995

14.5%

2003

15.6%

1996

14.6%

2004

18.4%

1997

17.1%

2005

17.7%

1998

15.8%

2006

17.0%

1999

16.0%

2007

17.8%

2000

15.5%

2008

17.1%

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