Question

Anystate Auto Insurance Company took a random sample of 376 insurance claims paid out during a 1-year period. The average claim paid was $1600. Assume σ = $262.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Answer 1

Sample size = n = 376

Sample mean = = 1600

Population standard deviation = = 262

We have to construct 90% confidence interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 1.64    ( Using z table)

So confidence interval is ( 1600 - 22.1591 , 1600 + 22.1591) = > ( 1577.84 , 1622.16)

lower limit	$1577.84
upper limit	$1622.16

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We have to construct a 99% confidence interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 2.58 ( Using z table)

So confidence interval is ( 1600 - 34.8600 , 1600 + 34.8600) = > ( 1565.14 , 1634.86)

lower limit	$1565.14
upper limit	$1634.86