Question

Anystate Auto Insurance Company took a random sample of 380 insurance claims paid out during a 1-year period. The average claim paid was $1525. Assume σ = $232.

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 = 380

Z/2 = 1.645

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

= 1.645 * (232 / 380)

Margin of error = E = 19.58

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

- E < < + E

1525 - 19.58 < < 1525 + 19.58

1505.42 < < 1544.58

Lower limit: $1505.42

upper limit: $1544.58

Sample size = n = 380

Z/2 = 2.576

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

= 2.576 * (232 / 380)

Margin of error = E = 30.66

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

- E < < + E

1525 - 30.66 < < 1525 + 30.66

1494.34 < < 1555.66

Lower limit: $1494.34

upper limit: $1555.66