Question: Some of the methods in this section are approximations rather than exact probability results. We have given rules of thumb for safe use of these approximations.

a) You are interested in attitudes toward drinking among the 75 members of a fraternity. You choose 25 members at random to interview. One question is "Have you had five or more drinks at one time during the last week?" Suppose that in fact 20% of the 75 member would say "Yes." Explain why you cannot safely use B(25, 0.2) distribution for the Count x in your sample who say "Yes."

b) The National AIDS Behavioral Surveys found that 0.2% (that's .002 as a decimal fraction) of adult heterosexuals had both received a blood transfusion and had a sexual partner from a group at high risk of AIDS. Suppose that this national proportion holds for your region. Explain why you cannot safely use the normal approximation for the sample
proportion who fall in this group when you interview an SRS of 500 adults.