Answer all questions with explanation

7. [5 marks] A survey of a random sample of 40 actuarial scientists who passed all their exams and are working in the field of actuarial sciences found the sample average salary to be $125,000 and the standard deviation to be $15,000. A. [3 marks] Find the 90% confidence interval for the true average salary of actuarial scientists. B. [2 marks] If it is desired to be 95% confident that the sample mean is within $4,000 of the true average salary of actuarial scientists, how many actuarial scientists should the survey have