The mean annual salary of classroom teachers is approximately normal with a mean of $45,915. Assume a standard deviation of $8000. Do the following for the variable “annual salary” of classroom teachers.

a) Determine the sampling distribution of the sample mean for sample of size 64.

The sample mean is

The sample standard deviation is

b) Determine the sampling distribution of the sample mean for samples of size 256.

The sample mean is

The sample standard deviation is

c) What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of the sample of 64 classroom teachers will be most $1000? (round to 4 decimal places)

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 256 classroom teachers will be at most $1000? ( round to 4 decimal place)