Questions: The trade magazine QSR routinely checks the dive through service times of fast-food restaurants. A 95% confidence interval that results from examining 696 customers in Taco Boirs drive-through has a lower bound of 1552 seconds and an upper bound of 1604 seconds. Complete parts (a) through (c) (a) What is the mean service time from the 696 customers? The mean service time from the 696 customers is 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 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 % confident that the mean drive-through service time of Taco Bell is between seconds and seconds B. One can be % confident that the mean drive-through service time of Taco Bell is seconds C. There is a %. probability that the mean drive-through service time of Taco Bell is between seconds and seconds. D. The mean drive through service time of Taco Bell is seconds % of the time.

The trade magazine QSR routinely checks the dive through service times of fast-food restaurants. A 95% confidence interval that results from examining 696 customers in Taco Boirs drive-through has a lower bound of 1552 seconds and an upper bound of 1604 seconds. Complete parts (a) through (c) (a) What is the mean service time from the 696 customers? The mean service time from the 696 customers is 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 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 % confident that the mean drive-through service time of Taco Bell is between seconds and seconds B. One can be % confident that the mean drive-through service time of Taco Bell is seconds C. There is a %. probability that the mean drive-through service time of Taco Bell is between seconds and seconds. D. The mean drive through service time of Taco Bell is seconds % of the time.
Transcript text: The trade magazine QSR routinely checks the dive through service times of fast-food restaurants. A $95 \%$ confidence interval that results from examining 696 customers in Taco Boirs drive-through has a lower bound of 1552 seconds and an upper bound of 1604 seconds. Complete parts (a) through (c) (a) What is the mean service time from the 696 customers? The mean service time from the 696 customers is $\square$ $\square$ 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 $\square$ $\square$ 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 between $\square$ seconds and $\square$ seconds B. One can be $\square$ \% confident that the mean drive-through service time of Taco Bell is $\square$ seconds C. There is a $\square$ \%. probability that the mean drive-through service time of Taco Bell is between $\square$ seconds and $\square$ seconds. D. The mean drive through service time of Taco Bell is $\square$ seconds $\square$ \% of the time.
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Solution

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Solution Steps

Step 1: Calculate the Mean Service Time

The mean service time (\(\bar{x}\)) is calculated as the midpoint between the lower and upper bounds of the confidence interval. Using the formula \(\bar{x} = \frac{L + U}{2}\), where \(L = 1552\) and \(U = 1604\), we find \(\bar{x} = 1578\) seconds.

Step 2: Determine the Margin of Error

The margin of error (\(E\)) is half the width of the confidence interval. Using the formula \(E = \frac{U - L}{2}\), where \(L = 1552\) and \(U = 1604\), we find \(E = 26\) seconds.

Step 3: Interpret the Confidence Interval

The interpretation of the confidence interval is as follows: We are 95% confident that the true mean service time of all customers lies within the interval from 1552 to 1604 seconds.

Final Answer:

The mean service time is 1578 seconds with a margin of error of 26 seconds. This means we are 95% confident that the true mean service time of all customers lies within the interval from 1552 to 1604 seconds.

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