(a). (12 points) Supposethe population is all homeownersin Virginia who rake/bag their leaves. Among these Virginia homeowners suppose the mean number of bags of leaves produced is 20.5 with a standard deviation of 4.9. There are a few Virginia homeowners who produce many bags of leaves and hence the distribution is skewed heavily to the right. If a simple random sample of 250 Virginia homeowners is selected and the number of bags of leaves produced is determined for each,describe completely the sampling distributionof , the resulting mean number of bags of leaves produced for this sample of 250 Virginia homeowners.

(b). (6 points) Consider the sampling distribution determined in part (a). What is the probability that = the mean number ofbags of leaves produced for this sample of 250 Virginia homeowners is less than 21?