A sample of n 16 scores is selected from a normal populatio

A sample of n = 16 scores is selected from a normal population with = 60 and = 20. What is the probability that the sample mean (M) will be greater than 50: p(M > 50)?

Solution

A sample of n = 16 scores is selected from a normal population with = 60 and = 20. What is the probability that the sample mean (M) will be greater than 50: p(M > 50)?

Standard error = sd/sqrt(n) =20/sqrt(16) =5

Z value for 50, z=(50-60)/5 = -2

P( M >50) = P( z > -2) = 0.9772