Question

Anystate Auto Insurance Company took a random sample of 368 insurance claims paid out during a 1-year period. The average claim paid was $1585. Assume σ = $242.

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,

= $1585

= $242

n = 368

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 * ( 242 / 368)

= 20.75

At 0.90 confidence interval estimate of the population mean is,

- E < < + E

1585 - 20.75 < < 1585 + 20.75

1564.25 < < 1605.75

(1564.25, 1605.75)

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 * ( 242 / 368)

= 32.50

At 0.99 confidence interval estimate of the population mean is,

- E < < + E

1585 - 32.50 < < 1585 + 32.50

1552.50 < < 1617.50

(1552.50, 1617.50)