127. An individual’s credit score is a number calculated based on that person’s credit history which helps a lender determine how much he/she should be loaned or what credit limit should be established for a credit card. An article in the Los Angeles Times gave data which suggested that a beta distribution with parameters A
150, B
850, a

8, b
2 would provide a reasonable approximation to the distribution of American credit scores. [Note: credit scores are integer-valued].

a. Let X represent a randomly selected American credit score. What are the mean value and standard deviation of this random variable? What is the probability that X is within 1 standard deviation of its mean value?

b. What is the approximate probability that a randomly selected score will exceed 750 (which lenders consider a very good score)?