You may need to use the appropriate appendix table or technology to answer this question. A random sample of 81 lunch customers was taken at a restaurant. The average amount of time these customers stayed in the restaurant was 42 minutes with a standard deviation of 27 minutes. (a) Compute the standard error (in minutes) of the mean. minutes (b) At a 95% confidence level, what statement can be made about the size of the margin of error? We can say with 0.95 probability that the distance between the sample mean of 42 minutes and the population mean is at most the margin of error calculated using the observed values above. Approximately 95% of all samples of size 81 will produce a sample mean and margin of error such that the distance between the sample mean and the population mean is equal to the margin of error. Approximately 95% of all samples of size 81 will produce a sample mean and margin of error such that the distance between the sample mean and the population mean is at least the margin of error. We can say with 0.95 probability that the distance between the sample mean of 42 minutes and the population mean is at least the margin of error calculated using the observed values above. Approximately 95% of all samples of size 81 will produce a sample mean and margin of error such that the distance between the sample mean and the population mean is at most the margin of error. (c) Construct a 95% confidence interval for the true average amount of time (in minutes) customers spent in the restaurant. (Round your answers to three decimal places.) minutes to minutes (d) At 95% confidence, how large of a sample (in customers) would have to be taken to provide a margin of error of 2.5 minutes? (Round your answer up to the nearest whole number.) customers