Suppose X is a Gamma random variable with a mean of 2028 and

Suppose X is a Gamma random variable with a mean of 20.28 and a standard deviation of 7.8. Determine the probability that X is larger than 15.

Show and explain how to do this type of problem. Thanks!

Solution

The probability is

P(X>15) = P((X-mean)/s >(15-20.28)/7.8)

=P(Z>-0.68)

=0.7517 (from standard normal table)