Question

A random sample of 42 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $17.29 per car. The population standard deviation is $5.22. Estimate the mean bill for all cars from the drive-thru with 97% confidence. Round intermediate and final answers to two decimal places

Answer 1

= Solution :

Given that,

sample mean = = 17.29

Population standard deviation =    = 5.22

Sample size n =42

At 97% confidence level the z is ,

= 1 - 97% = 1 - 0.97= 0.03

/ 2 = 0.03 / 2 = 0.015

Z/2 = Z0.015 = 2.170 ( Using z table )

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

= 2.170* ( 5.22 /  42 )

= 1.75
At 97% confidence interval
is,

- E < < + E

17.29 - 1.75 <   <17.29 + 1.75

15.54 <   < 19.04

(15.54 , 19.04)