Question

Anystate Auto Insurance Company took a random sample of 374 insurance claims paid out during a 1-year period. The average claim paid was $1600. Assume σ = $264. 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,

= $1600

= $264

n = 374

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* (264 / 374)

= 35.17

At 0.99 confidence interval estimate of the population mean is,

- E < < + E

1600 - 35.17 < < 1600 + 35.17

1564.83< < 1635.17

(1564.83 , 1635.17 )

lower limit = $ 1564.83

upper limit = $1635.17