Question

A chain fast food restaurant claims that customers spend an average of seven minutes waiting for service at the store. A random sample of 65 customers was timed at the store, and the average service time was found to be 8.5 minutes. Assume the standard devaition is 2 minutes per customer. a) Describe the sampling distribution of the mean waiting time. In particular, describe the type of distribution, its mean and its standard error. distribution name =......... mean =............... standared error =.............

Answer 1

The sampling distribution of the mean waiting time at the fast food restaurant is normally distributed with a mean of 7 minutes and a standard error of approximately 0.248.

Step-by-step explanation:

The sampling distribution of the mean waiting time for customers in a fast food restaurant, given a large enough sample size, is normally distributed according to the Central Limit Theorem. Since the population standard deviation is known and the sample size is sufficiently large (n=65), we can describe this sampling distribution with a mean (μ), which is equal to the population mean, and a standard error (SE) which is the population standard deviation (σ) divided by the square root of the sample size (n). In this case, the distribution name would be normal distribution, the mean would be 7 minutes (as claimed by the restaurant), and the standard error would be calculated as 2 minutes ÷ √65, which is approximately 0.248.