The following data set gives FICO credit scores of a sample of 40 mortgage applicants to a local bank. (Note that the scores are in increasing order for your convenience.)
444, 497, 502, 517, 532, 559, 568, 598, 611, 636,
637, 657, 681, 681, 693, 698, 701, 708, 711, 713,
714, 714,714, 739, 741, 743, 745, 753, 755, 768,
768, 781, 787, 792, 793, 797, 797, 809, 835, 836
Answer the question below.
(1) Calculate the mean and variance of this data set.
(2) The local bank requires that the applicant has a score of at least 600 in order to qualify for a certain low-rate mortgage. If one applicant is randomly selected from the sample above, what is the probability that the applicant is qualified for the low-rate mortgage?
(3) Assume that FICO score of all people in the United States have a normal distribution, and also assume that the mean and variance you calculated in question (1) are representative of the population mean and variance, respectively. If one person is randomly selected from the population, what is the probability that his/her score is at least 600?
(4) Under the assumption of (3), if 9 people are randomly selected from the population, what is the probability that they have an average score of at least 600?
(1) Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
(2,3) Z = (score-mean)/SD
Standard Deviation = square root of variance
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to your Z score.
I'll let you do the calculations.