Question

Anystate Auto Insurance Company took a random sample of 350 insurance claims paid out during a 1-year period. The average claim paid was $1555. 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,

Sample size = n = 350

Z/2 = 1.645

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

= 1.645 * (256 / 350)

Margin of error = E = 22.51

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

- E < < + E

1555 - 22.51 < < 1555 + 22.51

1532.49 < < 1577.51

lower limit: 1532.49

upper limit: 1577.51

Sample size = n = 350

Z/2 = 2.576

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

= 2.576 * (256 / 350)

Margin of error = E = 35.25

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

- E < < + E

1555 - 35.25 < < 1555 + 35.25

1519.75 < < 1590.25

lower limit: 1519.75

upper limit: 1590.25