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August 29, 2014

Homework Help: statistics

Posted by Carolyn on Wednesday, November 14, 2012 at 11:48am.

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?

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