Teacher Salaries. Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual...

Teacher Salaries. Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is $55.4 thousand. Assume a standard deviation of $9.2 thousand. Do the following tasks for the variable “annual
salary” of classroom teachers.

d. 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 $1000?
e. Repeat part (d) for samples of size 256