The credit scores of 32-year-old mortgage applicants at Directions Credit Union are normally distributed with a mean of 632 and a standard deviation of 102. Round your answers to four decimal places. (a) What is the probability that a randomly selected 32-year-old mortgage applicant has a credit score lower than 805?

(b) Find the credit score that defines the upper 3 percent.

(c) Seventy-nine percent of the 32-year-old mortgage applicants will have a credit score higher than what value?

(d) Within what range would the middle 87 percent of credit scores lie?

(e) What is the probability that a randomly selected 32-year-old mortgage applicant has a credit score higher than 735?

(f) What proportion of 32-year-olds applying for a mortgage have credit scores between 570 and 590?