Question: IRS records indicate that the mean deduction taken for charitable contributions by people with incomes between $25,000 and $80,000 is $1075. The amount deducted is normally distributed with a standard deviation of $150. What is the probability that the:

a. deduction for a single return selected at random is less than $1000?

b. average deduction for a sample of 9 returns is less than $1000?

c. average deduction for a sample of 25 returns is less than $1000?

d. average deduction for a sample of 49 returns is less than $1000?

e. Explain why the probability changes in parts b, c and d? What significance, if any, does this have for sampling?