Question

Anystate Auto Insurance Company took a random sample of 380 insurance claims paid out during a 1-year period. The average claim paid was $1525. 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

solution:-
given that mean = 1525
standard deviation = 258
sample n = 380

Find a 0.90 confidence interval for the mean claim payment
0.90 confidence for z is 1.645
confidence interval formula for z is
x +/- z * s/sqrt(n)
=> 1525 +/- 1.645 * 258/sqrt(380)
=> (1503.23 , 1546.77)
lower limit = 1503.23
upper limit = 1546.77

Find a 0.99 confidence interval for the mean claim payment
0.99 confidence for z i 2.58
confidence interval formula for z is
x +/- z * s/sqrt(n)
=> 1525 +/- 2.58 * 258/sqrt(380)
=> (1490.85 , 1559.15)
lower limit = 1490.85
upper limit = 1559.15