According to the Internal Revenue Service, the proportion of federal tax returns for which no tax was paid was p = 0.326. As part of a tax audit, tax officials draw a simple random sample of n = 120 tax returns.

a. What is the probability that the sample proportion of tax returns for which no tax was paid is less than 0.30?

b. What is the probability that the sample proportion of tax returns for which no tax was paid is between 0.35 and 0.40?

c. What is the probability that the sample proportion of tax returns for which no tax was paid is greater than 0.35?

d. Would it be unusual if the sample proportion of tax returns for which no tax was paid was less than 0.25?