Question

Anystate Auto Insurance Company took a random sample of 352 insurance claims paid out during a 1-year period. The average claim paid was $1535. Assume σ = $260.

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

Solution :

Given that,

Sample size = n = 352

Z/2 = 1.645

Margin of error = E = Z/2* ( /n)

= 1.645 * (260 / 352)

Margin of error = E = 22.80

At 90% confidence interval estimate of the population mean is,

- E < < + E

1535 - 22.80 < < 1535 + 22.80

1512.20 < < 1557.80

Lower limit: $1512.20

Upper limit: $1557.80

Sample size = n = 352

Z/2 = 2.576

Margin of error = E = Z/2* ( /n)

= 2.576 * (260 / 352)

Margin of error = E = 35.70

At 99% confidence interval estimate of the population mean is,

- E < < + E

1535 - 35.70 < < 1535 + 35.70

1499.30 < < 1570.70

Lower limit: $1799.30

Upper limit: $1570.70