The National Center for Educational Statistics reported that in 2009 the ACT college placement and admission examination had a mean of 21.1 and standard deviation of 5.1. (Source: Data from nces.ed.gov/programs/digest/d09/tables/dt09_147.asp.)
a. Which probability distribution would you expect to be most appropriate for describing the scores: the normal, or the binomial? Why?
b. A college requires applicants to have an ACT score in the top 20% of all scores. Using the distribution you chose in part a, find the lowest ACT score a student could get to meet this requirement.
c. Of five students picked at random from those taking the ACT, find the probability that none score high enough to satisfy the admission standard you found in part b.