A random sample of 49 lunch customers was taken at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 33 minutes. From past experience, it is known that the standard deviation equals 10 minutes.
a. Compute the standard error of the mean.
b. What can be said about the sampling distribution for the average amount of time customers spent in the restaurant? Be sure to explain your answer.
c. With a .99 probability, what statement can be made about the size of the margin of error?
d. Construct a 99% confidence interval for the true average amount of time customers spent in the restaurant.
e. With a .99 probability, how large of a sample would have to be taken to provide a margin of error of 2.5 minutes or less?