Practice Test 8
AP Statistics
Name:
Directions: Work on these sheets.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1. 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.
2. 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.
3. 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.
4. There are 10 patients on the neonatal ward of a local hospital who are monitored by 2 staff
members. If the probability of a patient requiring emergency attention by a staff member is 0.3,
what is the probability that there will not be sufficient staff to attend all emergencies? Assume
that emergencies occur independently.
(a) 0.3828
(b) 0.3000
(c) 0.0900
(d) 0.9100
(e) 0.6172
5.
In 1989 Newsweek reported that 60% of young children have blood lead levels that could impair
their neurological development. Assuming that a class in a school is a random sample from the
population of all children at risk, the probability that more than 3 children have to be tested until
one is found to have a blood level that may impair development is
(a) 0.064.
(b) 0.096.
(c) 0.64.
(d) 0.16.
(e) 0.88.
Chapter 8
1
Test 8A
6. 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.
7. A basketball player makes 70% of her free throws. She takes 7 free throws in a game. If the
shots are independent of each other, the probability that she makes the first 5 and misses the last 2
is about
(a) 0.635.
(b) 0.318.
(c) 0.015.
(d) 0.49.
(e) 0.35.
8. A cell phone manufacturer claims that 92% of the cell phones of a certain model are free of
defects. Assuming that this claim is accurate, how many cell phones would you expect to have to
test until you find a defective phone?
(a) 2, because it has to be a whole number
(b) 8
(c) 12.5
(d) 92
(e) 93
9. A dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck of 52 cards. Let
Y be the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the
following best describes this setting?
(a) Y has a binomial distribution with n = 40 observations and probability of success p = 0.5.
(b) Y has a binomial distribution with n = 40 observations and probability of success p = 0.5,
provided the deck is shuffled well.
(c) Y has a binomial distribution with n = 40 observations and probability of success p = 0.5,
provided after selecting a card it is replaced in the deck and the deck is shuffled well before
the next card is selected.
(d) Y has a normal distribution with mean p = 0.5.
(e) Y has a geometric distribution with n = 40 observations and probability of success p = 0.5.
10. A college basketball player makes 80% of her free throws. Suppose this probability is the same
for each free throw she attempts. The probability that she makes all of her first four free throws
and then misses her fifth attempt this season is
(a) 0.32768.
(b) 0.08192.
(c) 0.0064.
(d) 0.0032.
(e) 0.00128.
Chapter 8
2
Test 8A
11. The probability that a three-year-old battery still works is 0.8. A cassette recorder requires four
working batteries to operate. The state of batteries can be regarded as independent, and four
three-year-old batteries are selected for the cassette recorder. What is the probability that the
cassette recorder operates?
(a) 0.9984
(b) 0.8000
(c) 0.5904
(d) 0.4096
(e) The answer cannot be computed from the information given.
12. A random sample of 15 people is taken from a population in which 40% favor a particular
political stand. What is the probability that exactly 6 individuals in the sample favor this political
stand?
(a) 0.6098
(b) 0.5000
(c) 0.4000
(d) 0.2066
(e) 0.0041
13. It has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to
cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the
probability that the consumer will have more than 6 contaminated chickens?
(a) 0.961
(b) 0.118
(c) 0.882
(d) 0.039
(e) 0.079
14. Refer to the previous question. Suppose that a supermarket buys 1000 frozen chickens from a
supplier. The number of frozen chickens that may be contaminated that are within two standard
deviations of the mean is between A and B. The numbers A and B are
(a) (90, 510)
(b) (290.8, 309.2)
(c) (0, 730)
(d) (271, 329)
(e) (255, 345)
15. Suppose X has a geometric distribution with probability 0.3 of success and 0.7 of failure on each
observation. The probability that X = 4 is
(a) 0.0081.
(b) 0.0189.
(c) 0.1029.
(d) 0.2401.
(e) none of the above.
16. If X has a binomial distribution with n = 400 and p = 0.4, the Normal approximation for the
binomial probability of the event {155 < X < 175} is
(a) 0.6552.
(b) 0.6429.
(c) 0.6078.
(d) 0.6201.
(e) 0.6320.
Chapter 8
3
Test 8A
17. A basketball player makes 70% of her free throws. She takes 7 free throws in a game. If the
shots are independent of each other, the probability that she makes 5 out of the 7 shots is about
(a) 0.635.
(b) 0.318.
(c) 0.015.
(d) 0.329.
(e) 0.245.
18. A set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly and
you turn cards over, one at a time, beginning with the top card. Let X be the number of cards you
turn over until you observe the first red card. The random variable X has which of the following
probability distributions?
(a) The Normal distribution with mean 5
(b) The binomial distribution with p = 0.5
(c) The geometric distribution with probability of success 0.5
(d) The uniform distribution that takes value 1 on the interval from 0 to 1
(e) None of the above
Part 2: Free Response
Answer completely, but be concise. Write sequentially and show all steps.
19. Describe the four conditions that are required for a binomial setting.
20. A survey conducted by the Harris polling organization discovered that 63% of all Americans are
overweight. Suppose that a number of randomly selected Americans are weighed.
(a) Find the probability that the fourth person weighed is the first person to be overweight.
(b) Find the probability that it takes more than 4 people to observe the first overweight person.
(c) Find the mean and variance of the number of Americans that would have to be weighed in
order to find the first person that was overweight.
Chapter 8
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Test 8A
21. A headache remedy is said to be 80% effective in curing headaches caused by simple nervous
tension. An investigator tests this remedy on 100 randomly selected patients suffering from
nervous tension.
(a) Define the random variable being measured. X =
(b) What kind of distribution does X have?
(c) Calculate the mean and standard deviation of X.
(d) Determine the probability that exactly 80 subjects experience headache relief with this
remedy.
(e) What is the probability that between 75 and 90 (inclusive) of the patients will obtain relief?
Justify your method of solution.
22. The Ferrells have three children: Jennifer, Jessica, and Jaclyn. If we assume that a couple is
equally likely to have a girl or a boy, then how unusual is it for a family like the Ferrells to have
three children who are all girls? Let X = number of girls (in a family of three children).
(a) Construct a pdf (probability distribution function) table for the variable X.
(b) Construct a pdf histogram for X.
(c) Construct a cdf (cumulative distribution function) table for X.
(d) Construct a cdf histogram for X.
Chapter 8
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Test 8A
(e) What is the probability that a family like the Ferrells would have three children who are all
girls?
23. Would most wives marry the same man again, if given the chance? According to a poll of 608
married women conducted by Ladies Home Journal (June 1988), 80% would, in fact, marry their
current husbands. Assume that the women in the sample were randomly selected from among all
married women in the United States. Does the number X in the sample who would marry their
husbands again have a binomial probability distribution? Explain.
24. A quarterback completes 44% of his passes.
(a) Explain how you could use a table of random digits to simulate this quarterback attempting 20
passes.
(b) Explain how you could use a TI-83/84/89 to simulate this quarterback attempting 20 passes.
(c) Using your scheme from either (a) or (b), simulate 20 passes. If you use the random digit
table, begin on line 149. If you use the TI-83/84/89, first enter 149rand to seed your
random number generator, and indicate which one you use. List the numbers generated and
circle the “successes.” Calculate the percent of passes completed.
Line 149
71546
05233
53946
68743
72460
27601
45403
88692
Line 150
07511
88915
41267
16853
84569
79367
32337
03316
(d) What is the probability that the quarterback throws 3 incomplete passes before he has a
completion?
Chapter 8
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Test 8A
(e) How many passes can the quarterback expect to throw before he completes a pass?
(f) Use two methods to determine the probability that it takes more than 5 attempts before he
completes a pass.
(g) Construct a probability distribution table (out to n = 6) for the number of passes attempted
before the quarterback has a completion.
(h) Sketch a probability histogram (out to n = 6) for the table you constructed in the previous
problem.
Chapter 8
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Test 8A