The number of facets in the eye of the fruit fly Drosophila melanogaster is of interest in genetics to model changes across many generations (ie genetic selection). The distribution of the number of facets in the eye in a certain Drosphila population has been welldocumented over a long period of time. The distribution is moderately positively skewed with a mean of 68 and a standard deviation of 22.

a) Estimate the probability of an individual fruit fly having 80 or more facets in the eye? How sure are you of this answer and why? In one state, a study was done that counted eye facets in 64 fruit fly of this species.

b) Given the population information above, describe the shape, mean and standard deviation of the sampling distribution of for samples of this size?

c) How valid is this calculation in b)? State the concept or theory that is involved in this situation.

d) Sketch this sampling distribution, clearly labelling the horizontal axis.

e) What is the probability that the average number of eye facets is 80 or more for this sample size of 64?

f) On the same sketch in part d) above sketch the distribution that would result for the same population if the sample size was n = 256.