Yes, I believe it is.Assume that the population of men's weights are normally distributed with a mean of 172 lbs and a standard deviation of 29lbs. 36 men are randomly selected. What is the probability that their MEAN weight is less than 167lbs?

Is my answer right? Thanks.

My work:

z = (167-172) / (29 / square root of (36)) = -1.03

z = -1.03 =======> standard z scare table area is .3485

P ( mean weight less than 167) = .5000 - .3485 = .1515 =15.15%