Question

Anystate Auto Insurance Company took a random sample of 356 insurance claims paid out during a 1-year period. The average claim paid was $1540. Assume σ = $230.

A) Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$ ___
upper limit	$ ___

b) 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,

A)

Sample size = n = 356

Z_/2 = 1.645

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

= 1.645 * (230 / 356)

= 20.05

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

- E < < + E

1540 - 20.05 < < 1540 + 20.05

1519.95 < < 1560.05

lower limit $1519.95

upper limit $1560.05

b)

Sample size = n = 356

Z_/2 = 2.576

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

= 2.576 * (230 / 356)

= 31.40

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

- E < < + E

1540 - 31.40 < < 1540 + 31.40

1508.60 < < 1571.40

lower limit $1508.60

upper limit $1571.40