Question

Anystate Auto Insurance Company took a random sample of 350 insurance claims paid out during a 1-year period. The average claim paid was $1590. Assume σ = $234.

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 =$1590  
Population standard deviation=$234
Sample size=350  

Confidence interval formula by Z

a 0.90 confidence interval for the mean claim payment
Z critical value for 0.90 confidence level is 1.645

=>(1569.43,1610.57)

Lower confidence limit =$1569.43
Upper confidence limit =$1610.57

a 0.99 confidence interval for the mean claim payment
Z critical value for 0.99 confidence level is 2.58

=>(1557.78,1622.22)

Lower confidence limit =$1557.78
Upper confidence limit =$1622.22