If X is a normal random variable with standard deviation 4.00, and if the probab

Question

If X is a normal random variable with standard deviation 4.00, and if the probability that X is more than 5.52 is .1271 (as shown below), then what is the mean of X? (Note: the diagram is not necessarily to scale.)

If X is a normal random variable with standard deviation 4.00, and if the probability that X is more than 5.52 is .1271 (as shown below), then what is the mean of X? (Note: the diagram is not necessarily to scale.)

Explanation / Answer

The probability is P(X>5.52)=0.1271 --> P((X-mean)/s P(Z(5.52-mean)/4=1.14 (check standard normal table) --> 5.52-mean= 1.14*4=4.56 --> mean=5.52-4.56=0.96

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