Question

Anystate Auto Insurance Company took a random sample of 378 insurance claims paid out during a 1-year period. The average claim paid was $1545. Assume σ = $236.

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 = 378

Z/2 = 1.645

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

= 1.645 * (236 / 378)

Margin of error = E = 19.97

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

- E < < + E

1545 - 19.97 < < 1545 + 19.97

1525.03 < < 1564.97

Lower limit: $1525.03

Upper limit: $1564.97

Sample size = n = 378

Z/2 = 2.576

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

= 2.576 * (236 / 378)

Margin of error = E = 31.27

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

- E < < + E

1545 - 31.27 < < 1545 + 31.27

1513.73 < < 1576.27

Lower limit: $1513.73

Upper limit: $1576.27