The manager of The Cheesecake Factory in Boston reports that

The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 240, 185, 165, 180, 130, and 120. She believes that the number of customers served on weekdays follows a normal distribution. Construct a 99% confidence interval of the average number of customers served on weekdays. Use Table 2. (Round your intermediate calculations to 4 decimal places, \"sample mean\" and \"sample standard deviation\" to 2 decimal places and \"t\" value to 3 decimal places, and final answers to 2 decimal places.)

Solution

sample size n=6

sample mean= 170

sample standard deviation =43.24

The degree of freedom =n-1=6-1=5

Given a=1-0.99= 0.01, t(0.005, df=5) =4.032 (from student t table)

So the lower bound is

xbar - t*s/vn =170 - 4.032*43.24/sqrt(6) = 98.82

So the upper bound is

xbar + t*s/vn =170 + 4.032*43.24/sqrt(6) =241.18