1. A medical laboratory receives 30 blood specimens to check for HIV. Ten actually contain HIV. A worker is accidentally exposed to five specimens.
a. What is the probability that none contained HIV?
b. Fewer than three?
c. At least two?
2. J.D. Power and Associates says that 50 percent of car buyers now use the Internet for research and price comparisons.
a. Find the probability that in a sample of 8 car buyers, all 8 will use the Internet.
b. Find the probability that in a sample of 8 car buyers, at least 5 will use the Internet.
c. Find the probability that in a sample of 8 car buyers, more than 4 will use the Internet.
d. Find the mean and standard deviation of the probability distribution.
3. In a major league baseball game, the average is 0.6 broken bat per game.
a. Find the probability of no broken bats in a game.
b. Find the probability of at least 2 broken bats in a game.
4. Historically, 9 percent of a mail-order firm's repeat charge-account customers have an incorrect current address in the firm's computer database.
The number of customers out of 16 who have an incorrect address in the database is a binomial random variable with n = 16 and π = 0.09.
a. What is the probability that none of the next 16 repeat customers who call will have an incorrect address?
b. What is the probability that five customer who call will have an incorrect address?
c. What is the probability that six customers who call will have an incorrect address?
d. What is the probability that fewer than seven customers who call will have an incorrect address?
4. At an outpatient mental health clinic, appointment cancellations occur at a mean rate of 1.1 per day on a typical Wednesday. Let X be the number of cancellations on a particular Wednesday.
a. What is the probability that no cancellations will occur on a particular Wednesday?
b. What is the probability that one cancellations will occur on a particular wednesday?
c. What is the probability that more than two cancellations will occur on a particular wednesday?
d. What is the probability that four or more cancellations will occur on a particular wednesday?