# The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the...

The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 175, 125, 180, 220, 240, and 245. She believes that the number of customers served on weekdays follows a normal distribution. Construct the 99% confidence interval for the average number of customers served on weekdays. Use Table 2. (Round intermediate calculations to 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval to

First enter Data into EXCEL

We have to find the sample mean.

Excel command is =AVERAGE(Select data)

sample mean =$\bar{x}$ = 197.5

Now we have to find sample standard deviation.

Excel command is =STDEV(Select data)

standard deviation = s = 46.13

n = 6

$\bar{x}$ = 197.5

s = 46.13

99 % confidence interval

Formula

$(\bar{x}-E , \bar{x}+E)$

$E = \frac{tc*s}{\sqrt{n}}$

tc =4.032 ( using t-table )

$E = \frac{4.032*46.13}{\sqrt{6}}$

$E = 75.9326$

99 % confidence interval is

$(197.5-75.9326 , 197.5+75.9326)$

$(121.56 , 273.44)$

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