Question

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.

Answer #1

Given the distribution of the number of facets in the eye in a certain Drosphila population has been well documented over a long period of time. The distribution is moderately positively skewed with a mean of and a standard deviation of .

a) Assuming normal distribution the probability,

b)The sampling distribution has mean .

The sampling distribution is approximately normal with mean and sd .

c)Central Limit Theorem (CLT) says that the distribution of is approximately normal with mean and sd when is large.

d) The distibution of is plotted below.

e) The probability,

f) For , the distibution of is plotted below.

The common fruit fly, Drosophila melanogaster, is the most
studied organism in genetic research because it is small, easy to
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thorax length shorter than
a. 0.878 mm.
b. 0.633 mm.
c. 0.722 mm.
d. 0.644 mm.

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