Question

Anystate Auto Insurance Company took a random sample of 390 insurance claims paid out during a 1-year period. The average claim paid was $1545. Assume σ = $258.

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

We have given that,                              
                              
Sample mean =$1545                      
Population standard deviation=$258                  
Sample size=390                      
                      
                              
Confidence interval formula is

i) Level of significance =   1-0.90=0.1                      
Z critical value (by using Z table)=1.645
Therefore, a 0.90 confidence interval for the mean claim payment.

=(1523.51,1566.49)                          
                              
Lower confidence limit =$1523.51              
Upper confidence limit =$1566.49

ii)
Level of significance =   1-0.99=0.01                      
Z critical value (by using Z table)=2.58
Therefore, a 0.99 confidence interval for the mean claim payment.

=(1511.35,1578.65)          

Lower confidence limit =$1511.35
Upper confidence limit =$1578.65