Problem:

The Ajax Corporation would like to know the average age of its employees. The average age of a sample of 100 employees is 28 years with a standard deviation of 6.5 years.

Question 1) What is the 90% confidence interval for the average age of all the employees? (Round this answer to the nearest whole number.)

Question 2) How many employee records need to be checked to increase the confidence to 95% with the same interval (range)?

Question 3) 32% of the sampled employees from the Ajax Corporation have been employed for at least 60 months. What is the 95% confidence interval for the proportion of employees that have average employment of at least 60 months?

Question 4) How may employee records need to be checked to for the company to be 90% confident that its estimated proportion was within 5%?

Solve the given numerical problem and illustrate step by step calculation.