Question 1. Confidence Intervals for a Population Mean when is known

Several business-related job positions have been reviewed. 40 randomly selected job adverts report the following salaries (expressed in thousands of ):

[49 47 39 42 31 40 42 44 45 39 51 47 42 35 49 48 36 41 48 44 43 39 52 42 37 45 49 47 49 43]

Assuming that the population standard deviation is equal to 4.6, find a:

90% confidence interval for the mean salary;

95% confidence interval for the mean salary; and a

99% confidence interval for the mean salary.