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...




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For a random sample of 256 owners of medium-sized cars, it was found that their<br>average monthly car insurance premium for comprehensive cover was R356.<br>Assume that the population standard deviation is R44 per month and that insurance<br>7<br>premiums are normally distributed.<br>(a) Find the 95% confidence interval for the average monthly comprehensive car<br>insurance premium paid by all owners of medium-sized cars. Interpret the<br>result. (Use the z-table.)<br>(b) Find the 90% confidence interval for the same problem. Interpret the<br>result and compare it to (a).<br>(c) Compute (a) using Excel's NORMSINV formula to find the z-value.<br>(d) Use Excel's CONFIDENCE formula to compute (a).<br>(e) If 3 000 car owners are comprehensively insured by the Sun Insurance<br>company, estimate, with 95% confidence, the total monthly premium income<br>of the company.<br>

Extracted 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.

Jun 10, 2022
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