Given an unspecified distribution of x's with mean = 109 and standard
deviation = 17, a random sample of size 20 is taken. Find the
probability that the sample mean is greater than 107.

Solution using Minitab:

sigma-xbar = 17/sqrt(20) = 3.80131556175

t-xbar = (107-109)/3.80131556175 = -2/3.80131556175 = -0.526133641765

calc / prob. dist / t Distribution
 
Cumulative Distribution Function 

Student's t distribution with 19 DF

        x  P( X <= x )
-0.526134     0.302442

1-0.302442 = 0.697558

We simulate this problem by generating random data that has the mean and
standard deviation given above.

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