Question

Anystate Auto Insurance Company took a random sample of 386 insurance claims paid out during a 1-year period. The average claim paid was $1550. Assume σ = $230.

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,

a) Z/2 = Z0.05 = 1.645

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

= 1.645 * ( 230 /  386 )

= 19.26

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

  ± E   

= 1550  ± 19.26

= ( 1530.74, 1569.26 )

lower limit = $ 1530.74

upper limit = $ 1569.26

b) Z/2 = Z0.005 = 2.576

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

= 2.576 * ( 230 /  386 )

= 30.16

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

  ± E   

= 1550  ± 30.16

= ( 1519.84, 1580.16 )

lower limit = $ 1519.84

upper limit = $ 1580.16