Statistics Probability

Question

A manufacturer knows that their items have a normally distributed length with a mean of 17.4 inches, and a standard deviation of 1.4 inches. if 13 items are chosen at random what is the probability that their mean is less than 17 inches?

Answer 1

z = (sample mean - pop mean)/(pop std dev/sqrt(sample size))

compute z = (17 - 17.4)/(1.4/sqrt(13)) = -1.03

P(xbar < 17) = P(z < -1.03)

from standard normal probability table: P(z < -1.03) = 0.1515