Question

Anystate Auto Insurance Company took a random sample of 372 insurance claims paid out during a 1-year period. The average claim paid was $1555. Assume σ = $250.

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 mean = $1555 , standard deviation σ = $250

sample n = 372

=> the value of 0.90 confidence interval from z table is 1.645

confidence interval formula

=> mean +/- z * standard deviation/sqrt(n)

=> 1555 +/- 1.645 * 250/sqrt(372)

=> (1533.68,1576.32)

lower limit = 1533.68

upper limit = 1576.32

---------------------------------------

=> the value of 0.99 confidence interval from z table is 2.58

confidence interval formula

=> mean +/- z * standard deviation/sqrt(n)

=> 1555 +/- 2.58 * 250/sqrt(372)

=> (1521.56 , 1588.44)

lower limit = 1521.56

upper limit = 1588.44