For a random sample of 256 owners of medium-sized cars, it was found that their average monthly car insurance premium for comprehensive cover was R356. Assume that the population standard deviation is R44 per month and that insurance premiums are normally distributed.
(a) Find the 95% confidence interval for the average monthly comprehensive car insurance premium paid by all owners of medium-sized cars. Interpret the result. (Use the z-table.)
(b) Find the 90% confidence interval for the same problem. Interpret the result and compare it to (a).
(c) Compute (a) using Excel's NORMSINV formula to find the z-value.
(d) Use Excel's CONFIDENCE formula to compute (a).
(e) If 3 000 car owners are comprehensively insured by the Sun Insurance company, estimate, with 95% confidence, the total monthly premium income of the company.