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 $1505. Assume σ = $256.

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,

= 1505

= 256

n = 40

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 * (256 / 352 )

= 22.44

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

- E < < + E

1505 - 22.44 < < 1505 + 22.44

1482.56 < < 1527.44

Lower limit =1482.56$

Upper limit = 1527.44$

b ) At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

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

= 2.576 * (256 / 352 )

= 35.15

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

- E < < + E

1505 - 35.15 < < 1505 + 35.15

1469.85 < < 1540.15

Lower limit =1469.85$

Upper limit = 1540.15$