Suppose a random sample of size 36 is drawn from a populatio

Suppose a random sample of size 36 is drawn from a population with a mean of 279. If 87% of the time the sample mean is less than 282, what is the population standard deviation?

Solution

As for a left tailed area of 0.87, the z score is

z = 1.126391129

Thus, as

sigma = (X-u)*sqrt(n)/z

Then

sigma = (282 - 279)*sqrt(36)/1.126391129

sigma = 15.98023949 [ANSWER]