Question

Anystate Auto Insurance Company took a random sample of 370 insurance claims paid out during a 1-year period. The average claim paid was $1535. Assume σ = $254.

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,

=1535

= 254

n = 370

a ) At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * (254/ 370 )

= 21.72

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

- E < < + E

1535 - 21.72 < < 1535 + 21.72

1513.28 < < 1556.72

Lower limit =1513.28

Upper limit = 1556.72

b ) At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z 0.005 = 2.576

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

= 2.576 * (254/ 370 )

= 34.01

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

- E < < + E

1535 - 34.01 < < 1535 + 34.01

1500.99 < < 1569.01

Lower limit =1500.99

Upper limit =1569.01