Chapter 10

10. a.

Probability Distributions

y 0.3

Lesson 10-4 (pp. 637-644)

0.2 0.1

Mental Math

3.6

1

2

3

4

5

6

x

Questions

1. 1

b. about 1.97

2. False; The mean of the random variable is the probability-weighted mean of the possible outcomes. The mean can differ from the possible outcomes.

11. a.

5. Not a probability distribution.

8. a. –5 –4 –3 –2 –1

x

0

1

2

3

4

5

5 5 1 _ 1 _ 1 1 _ 1 _ 1 _ 1 _ 1 _ 1 _ _ _ P(x) _ 36 18 12 9 36 6 36 9 12 18 36

b.

y

0.2 0.1 -2

2

4

2

3

4

5

5 _ 18

2 _ 9

1 _ 6

1 _ 9

1 _ 18

12. a. It is the amount you make if you buy a ticket and don’t win (in total you lose 1 dollar). 122 _ b. 125 c. –1; winning nothing 1 d. – _ 5 13. a. about 3.64 years b. about 1.88 c. about 1.37 years 14. A and D 15. a. 1, 7, 21, 35, 35, 21, 7, 1; all are divisible by 7 except the first and last. b. 1, 9, 36, 84, 126, 126, 84, 36, 9, 1; 84 is not divisible by 9. n! c. nCr = _ r!(n - r)! ; We know that n is prime and r and (n - r) are smaller than n, so any part of r! multiplied times any part of (n - r)! will never equal (and thus never cancel) n from the numerator.

0.3

-4

1

b. about 1.94; because 1.97 was the mean of the relative frequencies c. about 2.05 d. about 1.43

4. P is a probability distribution. The mean of the random variable is 3.

7. a. the number of days of incubation time b. about 3.92 days c. x = 5

1 _ 6

P(x)

3. Not a probability distribution.

6. P is a probability distribution. The mean of the random variable is 2.47.

x 0 (Difference)

x

16. 17th term: 43C16 = 265,182,149,218; 21st term: 43C20 = 960,566,918,220

c. 0 9. a. about 1.72 b. about 1.31

17. 6C3 = 20 18. 10! = 3,628,800 19. a. and b.

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Back to Lesson 10-4

c. There is insufficient evidence to reject the hypothesis that the coin is fair because 0.011 > 0.01. 20. 3P3 · 5P5 = 720 21. a. Answers vary. Sample: The life expectancy for a 20 year-old male in the United States is 56.2 years, for a total lifetime of 76.2 years. b. Life expectancies are determined by measuring the probability of surviving from one year to the next for all relevant ages. These are used to create a “life table.” The life expectancy is the mean of the random variable, in this case life expectancy.

A193

Functions, Statistics, and Trigonometry

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Vendor: STET

Volume: 2

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