Question

Fast-Food Bills for Drive-Thru Customers A random sample of 47 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $16.88 per car. The population standard deviation is $5.64. Estimate the mean bill for all cars from the drive-thru with 92% confidence. Round intermediate and final answers to two decimal places.

Answer 1

To estimate the mean bill for all cars from the drive-thru with 92% confidence, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value) × (Standard Deviation / √Sample Size). Given the provided values, rounding to two decimal places, the estimated mean bill for all cars from the drive-thru with 92% confidence is $16.88 ± $1.36.

Step-by-step explanation:

To estimate the mean bill for all cars from the drive-thru with 92% confidence, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) × (Standard Deviation / √Sample Size)

Given that the sample mean is $16.88, the population standard deviation is $5.64, and the sample size is 47, we need to calculate the critical value for a 92% confidence level. Looking up the critical value in a t-table with 46 degrees of freedom, we find it to be approximately 1.68.

Substituting these values into the formula:

Confidence Interval = $16.88 ± (1.68) × ($5.64 / √47)

Rounding to two decimal places, the estimated mean bill for all cars from the drive-thru with 92% confidence is $16.88 ± $1.36.