For SOA actuarial Exam P. candidates receive their grades ranging from 0 to 10.

Question

For SOA actuarial Exam P. candidates receive their grades ranging from 0 to 10. 90 days after the exam date. A candidate passes the Exam P with a grade of 6 or above. The (fictional) grade distribution for passing candidates worldwide of May 2015 exam is summarized in the following table. Denote the passing grade as random variable X, mu x as the expected value of X and sigma x as the standard deviation of X Calculate mu x and sigma x. Evaluate the probability (X - mu x | sigma x). Suppose a university has 10 passing candidates in the May 2015 exam and their grades are the following: 7.6,7,6,8,10,9,7,8,7 The university does not have the passing grade distribution table for the worldwide candidates, so it decides to use the passing grades of its 10 students to estimate the mean as X and estimate the standard deviation as s. Calculate X and s.

Explanation / Answer

b)

Prob (|x-mux|<sigma)

= 418/1178 = 0.3548

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x bar = 7.5

std dev s = 1.20416

Grade 6 7 8 9 10 Total Count 418 380 154 130 96 1178 f*x 2508 2660 1232 1170 960 8530 f*x^2 15048 18620 9856 10530 9600 63654 54.03565 Mean 7.241087 Variance 1.602319 sigma 1.265827

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