FOR INSTRUCTOR'S USE

1. (New England Journal of Medicine)For several years, evidence has been mounting that folic acid reduces major birth defects. A Hungarian study provides the strongest evidence yet.

For the study, the doctors enrolled 4753 women prior to conception. The women were divided randomly into two groups. One group took daily multivitamins containing 0.8 mg of folic acid, whereas the other group received only trace elements. A drastic reduction in the rate of major birth defects occurred among the women who took folic acid: 13 per 1000 as compared to 23 per 1000 for those women who did not take folic acid.

a. Is this an observational study or an experiment? Explain

b. If it is an experiment, define the experimental units, factor(s), levels of the factors, treatments, and the response variable.

c. If it is an experiment, discuss how the three main principles of the design of experiment are satisfied.

2. In 1996 Wisconsin Driver Survey, several variables were measured on each subject including

• Gender

• Attitude toward drunken driving

Attitude was measured by response to question "How serious a problem do you think drunk driving is in Wisconsin?" Possible answers were "extremely serious" and "not extremely serious". The following table summarizes the associated probabilities.

a. What is the probability that a randomly selected person thinks drunk driving is not an extremely serious problem?

b. What is the probability that a randomly selected person thinks drunk driving is an extremely serious problem or male?

c. If a male is selected, what is the probability that person thinks drunk driving is an extremely serious problem?

d. What is the probability that a randomly selected person is female given that s/he thinks drunk driving is an extremely serious problem?

e. Are the events "selecting a female" and "selecting a person who thinks drunk driving is not an extremely serious problem " independent? Are they disjoint? Please justify your answer.

3. A nuclear power plant has a fail-safe mechanism consisting of six protective devices that function independently. The probability of failure for the six devices are 0.3, 0.2, 0.2, 0.1, and 0.1. If an accident will take place if all the devices fail, find the probability of an accident.

4. The number of traffic accidents in a certain town during a week is a random variable with the following probability distribution

a. Find the probability that during a week there will be at most one accident.

b. Find the mean and the standard deviation.

c. If there were at least one accident during a week, what is the probability that there were 3 accidents.

5. According to the Arizona Chapter of the American Lung Association, 7% of the population has lung disease. Of those people having lung disease, 90% are smokers; and of those not having lung disease, 25% are smokers.

a. Determine the probability that a randomly selected person is a smoker

b. Determine the probability that a randomly selected smoker has lung disease.