Question

A random sample of 169 observations is to be drawn from a population with a mean of 80 and a standard deviation of 39. find the probability that the mean of the sample will exceed 85.

Answer 1

Mu=80, sigma=39, X=85
Z=(X-mu)/sigma = 5/39=0.128=0.13
P(X<=85)= 0.5517 (from Z-table)
so, P(X>85)=1-0.5517=0.4483 approx. thats 44.8% probability.