The Provost of LSU is interested in raising the admission criteria. He found that the high school GPAs of applicants to the LSU undergraduate programs arenormallydistributed with mean =3.28. He also found that 33% of applicants have their high school GPAs higher than 3.50.

a. For a random sample of 4 applicants to LSU, find the probability that only one of them has his/her high school GPA higher than 3.50.

b. What is the percentage of the applicants whose high school GPAs are lower than 3.00?

c. For a random sample of 25 applicants to LSU, find the probability that the sample mean of their GPAs is higher than 3.50.

d. For a random sample of 25 applicants, find the probability that thesample standard deviationsof their GPAs is less than 0.588.