Question

Anystate Auto Insurance Company took a random sample of 358 insurance claims paid out during a 1-year period. The average claim paid was $1515. Assume σ = $248.

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:

Sample Size = n = 358

Sample mean =

Population Standard Deviation =

Part a) Find a 0.90 confidence interval for the mean claim payment

Formula:

where

c = 90% = 0.90

Area = ( 1+c)/2 = (1+0.90)/2=1.90/2=0.9500

Look in  z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Area 0.9495 corresponds to 1.64

Area 0.9505 corresponds to 1.65

Average of both z = (1.64+1.65)/2=1.645

Thus z_c = 1.645

Thus

Thus

Lower Limit = 1493.44

Upper Limit =1536.56

Part b)Find a 0.99 confidence interval for the mean claim payment.

Formula:

where

c = 99% = 0.99

Area = ( 1+c)/2 = (1+0.99)/2=1.99/2=0.9950

Look in  z table for Area = 0.9950 or its closest area and find corresponding z value.

​​​​​​

Area 0.9950 is between 0.9949 and 0.9951 and both the area are at same distance from 0.9950

Area 0.9949 corresponds to 2.57

Area 0.9951 corresponds to 2.58

Average of both z = (2.57+2.58)/2=2.575

Thus z_c = 2.575

Thus

Thus

Lower Limit = 1481.25

Upper Limit =1548.75