Download For problems 1-2, indicate whether a binomial distribution is a

AP STATISTICS
NAME___________________ # ____
QUIZ 8.1-8.2
I. Binomial, Geometric, or Neither?
For each of the following problems answer each of these questions. Does this follow a binomial distribution,
geometric distribution, or neither? How do you know (justify your answer specifically by addressing all 4
requirements)? If it is binomial or geometric what are the parameters? Do not calculate probabilities.
1. Among students who begin high school, 5% never graduate. We randomly select 15 people that
are no longer in high school. We are curious about how many of these 15 people we would expect
to have graduated.
2. 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 HIVpositive?
3. Consider a standard deck of 52 cards. We want to give each of five players a single card. After
giving each player a card we determine what color each player has and then put the cards back in
the deck to reshuffle. We are concerned with the number of players that get a red card each time.
We repeat this “game” seven times being certain to replace the cards in the deck and reshuffle
each time.
4. In high-profile discrimination court cases in the past, 76% of prospective jurors have been found
eligible to serve on juries (meaning there was 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 25th prospective juror who
is interrogated.
5. Assume you are taking a true-false final exam. There are 50 problems on the exam. Since you
have a 99 in the class you aren’t too concerned with the final so you elect to guess on all problems
without even reading the questions. You only need to get a 52 on the final to maintain your A in
the class.
6. Joey buys a Georgia lottery ticket every week. The back of the card says that he has a 1/999,999
chance of winning the jackpot each time he plays. He decides to continue playing every week
until he wins the big jackpot.
AP STATISTICS
NAME___________________ # ____
QUIZ 8.1-8.2
II. Finding Probabilities
Be certain to write out exactly what you typed into the calculator. Round answers to four decimal places.
Among employed men, 35% are divorced. Select 12 employed men at random.
7. What is the probability that exactly 2 of the 12 men are divorced?
8. What is the probability that 2 or more of the 12 men are divorced?
9. What is the probability that less than 5 of the 12 men are divorced?
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.
10. Determine the probability that the first 0 occurs as the fifth random digit generated.
11. How many random digits would you expect to have to generate in order to observe the first 0?
12. Construct a probability histogram for X = 1 through X = 5.
III. More Probability
Be certain to write out exactly what you typed into the calculator. Round answers to four decimal places.
The University of Georgia (UGA) claims that 80% of its basketball players get degrees (should be easy
enough considering some of the finals). An investigation examines the fate of all 20 players who entered
the program over a period of several years that ended six years ago. Of these players, 12 graduated and
the remaining 8 are no longer in school. If the university’s claim is true, the number of players that
graduate among the 20 should have the binomial distribution with n = 20 and p = 0.8.
13. Is it possible to use the normal approximation? If yes, then use normal calculations on at least one of
the next two problems. Give proof regardless of your answer.
14. What is the probability that between 12 and 15 out of 20 players graduate?
15. What is the probability that fewer than 12 out of the 20 players graduate?
AP STATISTICS
NAME___________________ # ____
QUIZ 8.1-8.2
IV. Even More Probability
Be certain to write out exactly what you typed into the calculator. Round answers to four decimal places.
There is a probability of 0.08 that a vaccine will cause a certain side effect. Suppose that a number of
patients are inoculated with the vaccine. We are interested in the number of patients vaccinated to
observe the first side effect.
16. Define the random variable of interest. X = ____________________________________________
17. Find the probability that exactly 5 patients must be vaccinated in order to observe the first side effect.
18. Construct a probability distribution table for X (don’t skip any numbers).
X
P(X)
19. Find the probability that the first side effect is observed when the 7th person is vaccinated.
20. Find the probability that the first side effect is observed before the 4th person is vaccinated.
21. Find the probability that between 6 & 10 (inclusive) patients must be vaccinated in order to observe
the first side effect.
22. How many patients would you expect to have to vaccinate in order to observe the first side effect?
What is the standard deviation for this geometric distribution?