Question

Anystate Auto Insurance Company took a random sample of 384 insurance claims paid out during a 1-year period. The average claim paid was $1575. Assume σ = $248.

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

a)

90% Confidence Interval :-
X̅ ± Z( α /2) σ / √ ( n )
Z(α/2) = Z (0.1 /2) = 1.645
1575 ± Z (0.1/2 ) * 248/√(384)
Lower Limit = 1575 - Z(0.1/2) 248/√(384)
Lower Limit = 1554.18
Upper Limit = 1575 + Z(0.1/2) 248/√(384)
Upper Limit = 1595.82

b)

99% Confidence Interval :-
X̅ ± Z( α /2) σ / √ ( n )
Z(α/2) = Z (0.01 /2) = 2.576
1575 ± Z (0.01/2 ) * 248/√(384)
Lower Limit = 1575 - Z(0.01/2) 248/√(384)
Lower Limit = 1542.40
Upper Limit = 1575 + Z(0.01/2) 248/√(384)
Upper Limit = 1607.60