Expenditure per Student. According to a report on theestimates of school statisticsin a particular country, the mean expenditure

(public) per student is $10.94 thousand annually. Assume a standard deviation of $3.3 thousand. Do the following tasks for the variable

“expenditure per student”.

a. Determine the sampling distribution of the sample mean for samples of size 64. Interpret your answer in terms of the distribution of all possible sample mean expenditure per student for samples of 64 students.

b. Repeat part

(a) for samples of size 256.

c. Do you need to assume that expenditure per student are normally distributed to answer parts

(a) and (b)? Explain your answer.

d. What is the probability that the sampling error made in estimating the population mean expenditure per student by the mean expenditure of a sample of 64 students will be at most $1000?

e. Repeat part

(d) for samples of size 256.