Question

A pizza chain records how long it takes customers to receive their delivery orders. Suppose the distribution of these delivery times is strongly skewed to the right with a mean of 30 minutes and a standard deviation of 10 minutes. Management plans on calculating the mean delivery time from a random sample of 25 orders. We can assume independence between orders in the sample.

What is the probability that the mean delivery time from the sample of 25 orders xˉ is farther than 2 minutes from the population mean?

Answer 1

We cannot calculate this probability because the sampling distribution is not normal.

Explanation:

Since the parent population is not normally distributed, the small sample size will result in a sampling distribution that isn't normal.

Answer 2

The probability that the mean delivery time from the sample of 25 orders xˉ is farther than 2 minutes from the population mean cannot be calculated.

Explanation:

As given in the question statement, the distribution of delivery times is strongly skewed to the right. The population distribution is skewed to right. Too much skewed distribution can cause the statistical model to work ineffectively and affects its performance. The probability can also not be calculated because the sample size is too small. Small sample size affects the results and makes them less reliable because it results in a higher variability and likelihood of skewing the results.