Question

Anystate Auto Insurance company took a random sample of 382 insurance claims paid out during a 1-year period. the average claim paid was $1505. assume o=$234.

find a 0.90 confidence interval for the mean claim payment. (round to two decimal places)
lower limit...?
upper limit...?

find a 0.99 confidence interval for the mean claim payment. (round to two decimal places)
lower limit...?
upper limit...?

Answer 1

Sample size = n = 382

Sample mean = = 1505

Population standard deviation = = 234

We have to construct 90% confidenc interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 1.64   ( Using z table)

So confidence interval is ( 1505 - 19.6349 , 1505 + 19.6349) = > ( 1485.37 , 1524.63)

Now we have to construct 99% confidenc interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 2.58   ( Using z table)

So confidence interval is ( 1505 - 30.8890 , 1505 + 30.8890) = > (1474.11 , 1535.89)