When one generation reproduces to form the next, the frequencies of alleles in the population can change by chance from generation to generation in a process called random genetic drift. An experiment was carried out using a very large laboratory population of the common fruit fly, Drosophila melanogaster, in which two eye-color alleles (versions of a gene) were present, one red (the norm for these flies) and the other brown. The frequency of the red allele in this base population was 0.5. The researchers created a new group of flies containing 32 alleles by randomly sampling flies from this large population (Buri 1956). They created a second new group of 32 alleles by sampling again from the base population. They repeated this procedure until there were a large number of new populations, all containing 32 alleles. The frequency distribution of the proportions of red-eyed alleles in the new groups closely matched a binomial distribution with n=32 and p=0.5 

a. On average, what do we expect the mean proportion of the red-eyed allele to be in the new groups?

b. What should be the standard deviation among groups in the proportion of red-eyed alleles?

c. If a randomly chosen new group has 60% red-eyed alleles, what proportion of its alleles are for brown eyes?

d. What is the probability that a randomly chosen group will have exactly 50% red-eyed alleles?

e. What is the probability that a randomly chosen group will have 30 or more red-eyed alleles?