Question

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 136000 dollars. Assume the population standard deviation is 45000 dollars. Suppose you take a simple random sample of 95 graduates.

Find the probability that a single randomly selected salary that doesn't exceed 138000 dollars.
Find the probability that a sample of size n=95n=95 is randomly selected with a mean that that doesn't exceed 138000 dollars.
Enter your answers as numbers accurate to 4 decimal places.

Answer 1

We have n= 95, μ = 136000, σ= 45000

1. P(x≤138000) = P(x-μ/σ ≤ 138000-13000/45000)

= P(z ≤ 0.044)

= 0.5715

2. P(x≤138000) = P((x-μ)/(σ/√n) ≤ 138000-136000/4500/√95)

= P(z ≤ 0.4332)

= 0.6675