(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.

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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
7
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.
Transcribed Image Text: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 7 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.
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