Sampling Distribution: There are 350 workers in a firm, with an average age of 37.6 years and an 8.3 years of standard deviation.

Question

There are 350 workers in a firm that consists of the following:

-An average age of 37.6 years

-Standard deviation of 8.3 years

What is the probability that a random sample of 45 employees would have an average age of under 40 years?

Answer 1

The standard deviation of the sample mean is σ/√n * √((N-n)/(N-1))

Note the presence of the finite sample correction factor.

Thus, s =8.3/√35 * √((350-35)/(350-1)) =1.33286644165475

Then, if we use the CLT to say the distribution is approximately normal,

P(x-bar <= 40) = Φ((40-37.6)/1.33286644165475) = Φ((40-37.6)/1.33286644165475) =

Φ((40-37.6)/1.33286644165475) = Φ(1.80063052455609) = .9641