AP Stats Ch. 7/8 MC
1. Suppose X is a random variable with mean µ. Suppose we observe X many times and keep track of the
average of the observed values. The law of large numbers says that
(a) the value of µ will get larger and larger as we observe X.
(b) as we observe X more and more, this average and the value of µ will get larger and larger.
(c) this average will get closer and closer to µ as we observe X more and more often.
(d) as we observe X more and more, this average will get to be a larger and larger multiple of µ.
(e) None of the above.
2. In a population of students, the number of calculators owned is a random variable X with
P(X = 0) = 0.2, P(X = 1) = 0.6, and P(X = 2) = 0.2. The mean of this probability distribution is
(a) 0.
(b) 2.
(c) 1.
(d) 0.5.
(e) The answer cannot be computed from the information given.
3. Refer to the previous problem. The variance of this probability distribution is
(a) 1.
(b) 0.63.
(c) 0.5.
(d) 0.4.
(e) The answer cannot be computed from the information given.
4. The number of calories in a one-ounce serving of a certain breakfast cereal is a random variable with mean
110. The number of calories in a full cup of whole milk is a random variable with mean 140. For breakfast
you eat one ounce of the cereal with 1/2 cup of whole milk. Let Z be the random variable that represents the
total number of calories in this breakfast. The mean of Z is
(a) 110.
(b) 140.
(c) 180.
(d) 250.
(e) 195.
5. The weight of reports produced in a certain department has a Normal distribution with mean 60 g and
standard deviation 12 g. What is the probability that the next report will weigh less than 45 g?
(a) 0.1042
(b) 0.1056
(c) 0.3944
(d) 0.0418
(e) The answer cannot be computed from the information given.
A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening
to soothing music. Let X be the number of puzzles completed successfully by a subject. X had the following
distribution:
__
X
Probability
1
0.2
2
0.4
3
0.3
4_
0.1
6. Using the above data, what is the probability that a randomly chosen subject completes at least 3 puzzles in
the five-minute period while listening to soothing music?
(a) 0.3
(b) 0.4
(c) 0.6
(d) 0.9
(e) The answer cannot be computed from the information given.
7. Using the above data, P(X < 3) is
(a) 0.3.
(b) 0.4.
(c) 0.6.
(d) 0.9.
(e) The answer cannot be computed from the information given.
8. Using the above data, the mean µ of X is
(a) 2.0.
(b) 2.3.
(c) 2.5.
(d) 3.0.
(e) The answer cannot be computed from the information given.
9.
Which of the following random variables should be considered continuous?
(a) The time it takes for a randomly chosen woman to run 100 meters
(b) The number of brothers a randomly chosen person has
(c) The number of cars owned by a randomly chosen adult male
(d) The number of orders received by a mail-order company in a randomly chosen week
(e) None of the above
10. Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume
that X is Normal with mean $360 and standard deviation $50. What is the value of
P(X > $400)?
(a) 0.2119
(b) 0.2881
(c) 0.7881
(d) 0.8450
(e) The answer cannot be computed from the information given.
11. A business evaluates a proposed venture as follows. It stands to make a profit of $10,000 with probability 3/20, to
make a profit of $5000 with probability 9/20, to break even with probability 1/4, and to lose $5000 with probability
3/20. The expected profit in dollars is
(a) 1500.
(b) 0.
(c) 3000.
(d) 3250.
(e) –1500.
12. In a large population of college students, 20% of the students have experienced feelings of math anxiety. If
you take a random sample of 10 students from this population, the probability that exactly 2 students have
experienced math anxiety is
(a) 0.3020.
(b) 0.2634.
(c) 0.2013.
(d) 0.5.
(e) 1.
13. Refer to the previous problem. The standard deviation of the number of students in the sample who have
experienced math anxiety is
(a) 0.0160.
(b) 1.265.
(c) 0.2530.
(d) 1.
(e) 0.2070.
14. In a certain large population, 40% of households have a total annual income of at least $70,000. A simple
random sample of 4 of these households is selected. What is the probability that 2 or more of the households
in the survey have an annual income of at least $70,000?
(a) 0.3456
(b) 0.4000
(c) 0.5000
(d) 0.5248
(e) The answer cannot be computed from the information given.
15. A factory makes silicon chips for use in computers. It is known that about 90% of the chips meet
specifications. Every hour a sample of 18 chips is selected at random for testing. Assume a binomial
distribution is valid. Suppose we collect a large number of these samples of 18 chips and determine the
number meeting specifications in each sample. What is the approximate mean of the number of chips
meeting specifications?
(a) 16.20
(b) 1.62
(c) 4.02
(d) 16.00
(e) The answer cannot be computed from the information given.
16. In a group of 10 college students, 4 are business majors. You choose 3 of the 10 students at random and ask
their major. The distribution of the number of business majors you choose is
(a) binomial with n = 10 and p = 0.4.
(b) binomial with n = 3 and p = 0.4.
(c) not binomial and not geometric.
(d) geometric with p = 0.4.
(e) geometric with p = 0.4 and n = 10.
17. Government statistics tell us that 2 out of every 3 American adults are overweight. Let X = number of
Americans that are overweight. How large would an SRS of American adults need to be in order for it to be
safe to assume that the sampling distribution of X is approximately Normal?
(a) 3
(b) 9
(c) 15
(d) 18
(e) 30