1. Nine percent of men and 0.25% of women cannot distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic signals.
a. If six men are randomly selected for a study of traffic signal perceptions, find the probability that exactly two of them cannot distinguish between red and green. Use the binomial probability formula and verify that the assumptions are satisfied.
b. Researchers need at least 50 men with this type of colorblindness, so they randomly select 600 men for a study of traffic-signal perceptions. Estimate the probability that at least 50 of the men cannot distinguish between red and green. Is the result high enough so that the researchers can be very confident of getting at least 50 men with red and green colorblindness?
2. The New York State Health Department reports a 10% rate of the HIV virus for the "at-risk" population. In one region, an intensive education program is used in an attempt to lower that rate. After running the program, a follow-up study of 150 at-risk individuals is conducted.
a. Assuming that the program has no effect, find the mean and standard deviation for the number of HIV cases in groups of 150 at-risk people.
b. Among the 150 people in the follow-up study, 8% (or 12 people) tested positive for the HIV virus. If the program has no effect, is that rate unusually low? Does this result suggest that the program is effective?
3. In one year, there were 116 homicide deaths in Richmond, Virginia. Using the Poisson distribution, find the probability that the number of homicide deaths for a randomly selected day is:
a. 0
b. 1
c. 2
4. Each year, billions of dollars are spent at theme parks owned by Disney, Universal Studios, Sea World, Busch Gardens, and others. A survey of 1233 people who took trips revealed that 111 of them included a visit to a theme park (based on data from the Travel Industry Association of America).
a. Find the point estimate of the percentage of people who visit a theme park when they take a trip.
b. Find a 95% confidence interval estimate of the percentage of all people who visit a theme park when they take a trip.
5. In one study of 71 smokers who tried to quit smoking with nicotine patch therapy, 32 were not smoking one year after the treatment. Use a 0.10 significance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority (more than 50%) are smoking a year after the treatment. Do these results suggest that the nicotine patch therapy is not effective?
6. In one study of 71 smokers who tried to quit smoking with nicotine patch therapy, 41 were smoking one year after the treatment. Use the sign test with a 0.05 significance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority (more than 50%) are smoking a year after the treatment.