Question

Anystate Auto Insurance Company took a random sample of 390 insurance claims paid out during a 1-year period. The average claim paid was $1585. 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

Solution :

Given that,

= 1585

= 248

n = 390

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( /n)

= 2.576* (248 / 390)

= 32.35

At 99% confidence interval mean is,

- E < < + E

1585-32.35 < < 1585+32.35

1552.65< < 1617.35

LOWER LIMIT 1552.65

UPPER LIMIT 1617.35

(A)

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z_/2* ( /n)

= 1.645* (248 / 390)

= 20.66

At 90% confidence interval mean is,

- E < < + E

1585-20.66 < < 1585+20.66

1564.34< < 1605.66

LOWER LIMIT 1564.34

UPPER LIMIT 1605.66