Question

Anystate Auto Insurance Company took a random sample of 382 insurance claims paid out during a 1-year period. The average claim paid was $1530. 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,

= $1530

= $256

n = 382

A) At 0.90 confidence level the z is ,

  = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (256 / 382)

= 21.55

At 0.90 confidence interval estimate of the population mean is,

- E < < + E

1530 - 21.55 < < 1530 + 21.55

1508.45 < < 1551.55

Lower limit $1508.45

Upper limit $1551.55

B) At 0.99 confidence level the z is ,

  = 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 * (256 / 382)

= 33.74

At 0.99 confidence interval estimate of the population mean is,

- E < < + E

1530 - 33.74 < < 1530 + 33.74

1496.26 < < 1563.74

Lower limit $1496.26

Upper limit $1563.74