A university administration is interested in knowing what proportion of applicants will be accepted to be enrolled into the statistics program. Of a random sample of 85 applicants, 32 were accepted to be enrolled in the statistics program. Give your answers to the nearest 3 decimal places.

a) Calculate the margin of error for p, the true proportion of all applicants that will be accepted in this program.

b) Construct a 95% confidence interval for p. What is the lower bound of this interval?

c) Construct a 90% confidence interval for p. What is the upper bound of this interval?