The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served w
as 120, 130, 100, 205, 185, and 220. She believes that the number of customers served on weekdays follows a normal distribution. Construct the 90% confidence interval for the average number of customers served on weekdays. (You may find it useful to reference the t table. Round intermediate calculations to at least 4 decimal places. Round "sample mean" and "sample standard deviation" to 2 decimal places and "t" value to 3 decimal places and final answers to 2 decimal places.)
1 answer:
Answer:
143.31 < µ < 176.69
Step-by-step explanation:
The manager wants a 90% confidence interval based on the data. We are given 6 weekdays of data. We have to do 3 things:
1. Calculate the mean number of customers
2. Calculate the standard deviation of the number of customers
3. Construct the confidence interval
*For #1 and #2, see attached photo 1 for the calculations...
The sample mean is: 160
The sample standard deviation is: 20.29
The t-value we need is found using the t-distribution chart, with 5 degrees of freedom. Our t-value is: 2.015
*See attached photo 2 for construction of the confidence interval
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