The distribution of hourly salaries for employees at a company has a normal distribution with μ = $62.7 per hour and σ = $5.7 per hour. You intend to draw a random sample of size n=21.
a) Find the mean and standard deviation of the sampling distribution of the sample mean.
b) Find the probability that the sample mean salary is more than $65 per hour.
c) Calculate the standard error of the sample mean.
d) Find the 95% confidence interval for the sample mean salary.