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Chapter 6
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
1.
Family size can be represented by the random variable X. Determine the average family size.
2
.17
X
P(X)
3
.47
4
.26
5
.10
(a)
(b)
(c)
(d)
(e)
2.94
3.00
3.29
3.49
3.86
2.
The heights of married men are approximately normally distributed with a mean of 70 and a standard deviation of 3, while the
heights of married women are approximately normal distributed with a mean of 65 and a standard deviation of 2.5. Determine the
probability that a randomly selected married woman is taller than a randomly selected married men.
(a)
(b)
(c)
(d)
(e)
0.05
0.10
0.15
0.20
Cannot be determined from the given information.
3. Suppose the average height of policemen is 71 inches with a standard deviation of 4 inches, while the average for policewoman is 66
inches with a standard deviation of 3 inches. If a committee looks at all ways of pairing up one male with one female officer, what will
be the mean and standard deviation for the difference in heights for the set of possible partners?
(a)
(b)
(c)
(d)
(e)
Mean of 5 inches with a standard deviation of 1 inch.
Mean of 5 inches with a standard deviation of 3.5 inches.
Mean of 5 inches with a standard deviation of 5 inches.
Mean of 68.5 inches with a standard deviation of 1 inch.
Mean of 68.5 inches with a standard deviation of 3.5 inches.
4. A married couple decide they wish to start a family and they really want to have a baby girl. Because of financial considerations,
they decide they will have children until they have a girl or a total of 3 children. If the probability of having a boy or girl is equally
likely, determine the expected number of boys.
(a)
(b)
(c)
(d)
(e)
0.5
0.75
0.875
1
1.25
5. Which of the following are true statements?
I.
II.
III.
(a)
(b)
(c)
(d)
(e)
I and II
I and III
II and III
II and III
I, II, and III
By the law of large numbers, the mean of a random variable will get closer and closer to a specific value.
The standard deviation of a random variable is never negative.
The standard deviation of a random variable is 0 only if the random variable takes a lone single value.
Use the following information for questions 6-8. The independent random variables X and Y are defined by the following probability
distribution tables.
X
P(X)
1
.6
3
.3
6
.1
Y
P(Y)
2
.1
3
.2
5
.3
7
.4
6. Determine the mean of X+Y
(a) 7.2
(b) 8.4
(c) 5.1
(d) 9
(e) 4.3
7. Determine the standard deviation of 3Y + 5
(a)
(b)
(c)
(d)
(e)
.44
3.62
0
5.1
5.44
8. Determine the standard deviation of 4X - 5Y.
(a)
(b)
(c)
(d)
(e)
15.38
–2.76
11.05
10.62
cannot be determined from the given information
9. The amount of pollutants a factory dumps into a river is approximately normally distributed with a mean of 2.43 and a standard
deviation of 0.88 tons. What is the probability that it dumps more than 3 tons?
(a)
(b)
(c)
(d)
(e)
(f)
0.2578
0.2843
0.6500
0.7157
0.7422
0.2585
10. Which of the following is not true concerning discrete probability distribution?
(a)
(b)
(c)
(d)
(e)
The probability of any specific value is between 0 and 1, inclusive.
The mean of the distribution is between the smallest and largest value in the distribution.
The sum of all probabilities is 1.
The standard deviation of the distribution is between –1 and 1.
The distribution may be displayed using a probability histogram.
Part II – Free Response (Questions 11-12) – Show your work and explain your results clearly.
11. Suppose the probability that someone will make a major mistake on an income tax return is 0.2.
(a) An Internal Revenue Service (IRS) agent plans to audit twenty returns and determine how many had a major mistake.
i.
Define an appropriate assignment of random digits and using the given random number table, simulate (and clearly label) this
situation 4 times.
08424 44753 77377 28744 75592 08563 79140 92454
53645 66812 61421 47836 12609 15373 98481 14592
ii. Based on your results, what is the expected number of returns with a major mistake?
(b) An Internal Revenue Service (IRS) agent plans to audit as many returns as necessary until she finds one with a major mistake.
i. Define an appropriate assignment of random digits and using the given random number table, simulate (and clearly label) this
situation 10 times.
08424 44753 77377 28744 75592 08563 79 140 92454
53645 66812 61421 47836 12609 15373 98481 14592
ii.
Based on your results, what is the expected number of returns with a major mistake?
12. AP Statistics test scores on Random Variables are described by the following probability distribution.
Score
P(Score)
40
.1
50
.2
60
.3
70
.3
80
.1
(a) Determine the mean and variance of the Scores.
(b) Mr. Myers, in yet another act of benevolence, decides to scale the scores so his students will not be denied admission to the
college of their choice. He decides the actual grades will become: Grade = 1.5 * Score – 20 .
(i) Determine the mean and variance of the Grades.
(ii) Which Score(s), if any, did not increase?
(c) Suppose three Scores were randomly (and independently) selected.
(i) Determine the mean and variance of the total of the three Scores.
(ii) What is the probability that the average of the three scores is greater than 75?