Question

A local pizza place claims that they average a delivery time of 7.32 minutes. To test this claim, you order 11 pizzas over the next month at random times on random days of the week. You calculate the average delivery time and sample standard deviation from the 11 delivery times (minutes), and with the sample mean and sample standard deviation of the time (minutes), you create a 95% confidence interval of (7.648, 9.992). (delivery time is normally distributed). What is the sample mean of 11 delivery times?

Answer 1

A local pizza place claims that they average a delivery time of 7.32 minutes. To test this claim, we order 11 pizzas over the next month at random times on random days of the week. We calculate the average delivery time and sample standard deviation from the 11 delivery times (minutes). And we also create a 95% confidence interval of (7.648, 9.992).(delivery time is normally distributed).

Sample size = n = 11

Now we know that 95% confidence interval is given by,

[ Where, n = Sample Size, S = Sample SD, Sample mean ]

So by the question we get,

....................(1)

....................(2)

Now we solve this two equation by elimination method.

Adding equation (1) and (2) we get,

So we get, Sample mean = 8.82

Answer:- Sample mean of 11 delivery times is 8.82 minutes