Answer to Question #12159 in Statistics and Probability for Jonathan

Question #12159

A Harris Interactive national telephone poll in 2002 asked, "Do you think adults should be allowed to legally use marijuana for medical purposes, if their doctor prescribes it, or do you think that marijuana should remain illegal even for medical purposes." The results showed that 80 percent of respondents answered, "Yes, it should be legal for medical purposes." Assuming that this accurately reflects national attitudes, find the probability when eight Americans are chosen at random:
a. Exactly three said "Yes."
b. Six or fewer said "Yes."

Expert's answer

Using a formula for binomial distribution with p=0.8 we get P(x=3)=0.92%

P(x<=6)=1-P(x=7)-P(x=8)=1-50.33%=49.67%