Download Quiz 8 - Cypress HS

AP Statistics
Chapter 8 Review Packet
Name: _____________________________
Row: ______
Date: __________
1. Ladies Home Journal magazine reported in 1993 that 66% of all dog owners greet their dog before greeting
their spouse or children when they return home at the end of the workday. Suppose that 12 dog owners are
selected at random.
(a) Show that the four requirements for a binomial setting are satisfied.
(b) Define the random variable: X = ____________________________________________________
(c) Find the probability that exactly 7 of the 12 dog owners greet their dog first when they arrive home.
(d) Find the probability that at least 5 of the 12 dog owners greet their dog first when they arrive home.
(e) What is the expected number of dog owners who greet their dog first when they arrive home?
(f) Find the mean and standard deviation for the random variable X in this problem.
2. Describe the four conditions that are required for a binomial setting.
3. Describe the four conditions that are required for a geometric setting.
4. A manufacturer produces a large number of toasters. From past experience, the manufacturer knows that
approximately 2% are defective. In a quality control procedure, we randomly select 20 toasters for testing.
We want to determine the probability that no more than one of these toasters is defective.
(a) Is a binomial distribution a reasonable probability model for the random variable X? State your reasons
clearly.
(b) Determine the probability that exactly one of the toasters is defective.
(c) Define the random variable. X = ______________. Then find the mean and standard deviation for X.
(d) Find the probability that at most two of the toasters are defective. (Include enough details so that it can
be understood how you arrived at your answer.)
5. In parts (a) and (b), indicate whether a geometric distribution is a reasonable probability model for the
random variable X. Give your reasons in each case.
(a) Suppose that one of every 100 people in a certain community is infected with HIV. You want to
identify an HIV-positive person to include in a study of an experimental new drug. How many
individuals would you expect to have to interview in order to find the first person who is HIV-positive?
(b) In high-profile discrimination court cases in the past, 76% of prospective jurors have been found eligible
to serve on juries (that is, no objection by either the prosecution or the defense). We have 25 people in
the pool of potential jurors, and we want to know if we will be successful in finding 12 people to serve
on the jury from the pool. Specifically, we want to determine the probability that the 12th acceptable
juror is found by the time that the 25th prospective juror is interrogated.
6. When a computerized generator is used to generate random digits, the probability that any particular digit in
the set {0, 1, 2, . . . , 9} is generated on any individual trial is 1/10 = 0.1. Suppose that we are generating
digits one at a time and are interested in tracking occurrences of the digit 0.
(a) Determine the probability that the first 0
occurs as the fifth random digit generated.
(b) How many random digits would you expect to
have to generate in order to observe the first 0?
(c) Construct a probability distribution table and a probability distribution histogram for X = 1 through X = 5.
x
p(x)
7. 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.
8. In order for the random variable X to have a geometric distribution, which of the following conditions must
X satisfy?
I. np ≥ 10 and n(1 – p) ≥ 10
II. The number of trials is fixed.
III. Trials are independent.
IV. The probability of success has to be the same for each trial.
V. The n observations have to be a random sample.
(a) III and IV
(b) II, III, IV, and V
(c) I and III
(d) I, III, and V
(e) II and III
9. Suppose we select an SRS of size n = 100 from a large population having proportion p of successes. Let X
be the number of successes in the sample. For which value of p would it be safe to assume the sampling
distribution of X is approximately Normal?
(a) 0.01
(b) 1/9
(c) 0.975
(d) 0.9999
(e) All of these
10. 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
11. 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. After you draw the card, you then put it back in the
deck and reshuffle. 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.
12. 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 probability that X is greater than 2 is
(a) 0.125.
(b) 0.5.
(c) 0.25.
(d) 0.945.
(e) none of (a) to (d).
13. 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.
14. 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.
15. 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.
16. 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.
17. 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