The mean annual salary of public classroom teachers is $49,000. Assume the standard deviation is $9,200. Do the following for the variable "annual salary"of classroom teachers.
a) Determine the sampling distribution of the sample mean for samples of size 64.
b) Repeat part "a" for samples of size 256
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 a sample of 64 classroom teachers will be at most $1,000?
d) Repeat for samples of size 256