Problem
The trade magazine QSR routinely checks the drive-through service times of fast-food restaurants. A $90 \%$ confidence interval that results from examining 752 customers in Taco Bell's drive-through has a lower bound of 171.0 seconds and an upper bound of 177.2 seconds. Complete parts (a) through (c). (a) What is the mean service time from the 752 customers? The mean service time from the 752 customers is 174.1 seconds (Type an integer or a decimal. Do not round.) (b) What is the margin of error for the confidence interval? The margin of error is 3.1 seconds. (Type an integer or a decimal. Do not round.) (c) Interpret the confidence interval. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals. Do not round.) A. One can be $\square \%$ confident that the mean drive-through service time of Taco Bell is $\square$ seconds. B. The mean drive-through service time of Taco Bell is $\square$ seconds $\square \%$ of the time. C. There is a $\square \%$ probability that the mean drive-through service time of Taco Bell is between $\square$ seconds and $\square$ seconds. D. One can be $\square \%$ confident that the mean drive-through service time of Taco Bell is between $\square$ seconds and $\square$ seconds. Clear all Check answer Get more help .
Solution
Step 1 ：(a) The mean service time can be calculated by taking the average of the lower and upper bounds of the confidence interval. So, the mean service time from the 752 customers is \(\boxed{174.1}\) seconds.
Step 2 ：(b) The margin of error can be calculated by subtracting the mean from the upper bound of the confidence interval. So, the margin of error for the confidence interval is \(\boxed{3.1}\) seconds.
Step 3 ：(c) The interpretation of the confidence interval is a statement about the range in which we are confident the true mean lies, given the data we have. So, one can be $90\%$ confident that the mean drive-through service time of Taco Bell is between $171.0$ seconds and $177.2$ seconds.
