stathistics please help

Question

In a university faculty members’ annual salary has a mean μ = $50,000 and standard deviation of σ = $3,000. What is the probability that the mean annual salary of a random sample of 25 faculty member from this university is more than $ 52,000?

Find this probability and interpret it.

Answer 1

To answer this question you would assume that the sample is normal because of the large sample size (25)

You find the Z-score of the value (52,000) using a normal distribution with mean 50,000 and s.d. 3,000.

You would find the probability associated with the z score and use that to answer the questions

z-score: .667

p-value: .253

The probability that the mean annual salary of a random sample of 25 is .253 (25.3%)