thumbs up if correct! An individual's credit score is a number calculated based on that person's credit history that helps a lender determine how much he/she should be loaned or what credit limit should be established for a credit card. An article gave data which suggested that a beta distribution withparameters A = 250, B = 900, a = 7, ß= 3 would provide a reasonable approximation to the distribution of American credit scores.(a) Let X represent a randomly selected American credit score. What are the mean value and standard deviation of this random variable? (Round your standard deviation to three decimal places.)meanstandard deviationWhat is the probability that X is within 1 standard deviation of its mean value? (Round your answer to three decimal places.)(b) What is the approximate probability that a randomly selected score will exceed 800 (which lenders consider a very good score)? (Round your answer to three decimal places.)

The following information is given.A=250 , B= 900, =7, =3PDF of 4 parameter beta distribution is,The mean is calculated as followsThe variance is calculated as follows The standard deviation is as follows The Mean value is 705 and the standard deviation of this random variable is 89.810.The probability that is within 1 standard deviation of its mean value is as followsThe cumulative probability is calculated by using Excel function:Lower bound: "=BETADIST(615.19,7,3,250,900)"Upper bound: "=BETADIST(794.81,7,3,250,900)".The probability that is within 1 standard deviation of its mean value is 0.666.b)The probability that a randomly selected score will exceed 800 is as followsThe probability is calculated by using excel function as followsThe probability that a randomly selected score will exceed 800 is 0.149.aThe Mean value is 705 and the standard deviation of this random variable is 89.810.The probability that is within 1 standard deviation of its mean value is 0.666.bThe probability that a randomly selected score will exceed 800 is 0.149.