For SOA actuarial Exam P candidates receive their grades ran

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.

Solution

b)

Prob (|x-mux|<sigma)

= 418/1178 = 0.3548

-----------------------------------------------

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