Question

Find the probability and interpret the results. If​ convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about ​$ 61,000. A random sample of 40 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than ​$ 58,500​? Assume σ = 6,000.

Answer 1

Using Central limit theorem, the distribution of the sample mean is given here as:

The probability now is computed here as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.9960 is the required probability here.