The mean annual salary of classroom teachers is approximatel

The mean annual salary of classroom teachers is approximately normal with a mean of $45,753. Assume a standard deviation of $8,800. Do the following for the variable annual salary of classroom teachers.

What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64 classroom teachers will be at most $1,000?

Solution

z = (x-bar - )/(s/n)

z = -1000/1000 = -1 and again z = 1000/1000 = 1

P(Sampling error is at most $1000) = P(-1 < z < 1) = 0.6827