An IRS agent has 19 tax returns on her desk, of which 14 were filed using the short form (1040A). She randomly chooses eight returns to audit. Determine the probability of the following:

a. All eight were filed using the short form.

b. At least six were filed using the short form.

c. Explain why it is not possible for none of the tax returns to be filed using the short form.

d. Calculate the mean and standard deviation of this distribution.