The quality control specialist of a fast food restaurant wants to analyze the drive-thru service times during lunch. After reviewing the records of drive-thru service times between 11:00 AM and 2:00 PM, it is determined that the population distribution of lunch drive-thru service times is skewed right with a mean of 174.6 seconds and a standard deviation of 88.7 seconds.

a. calculate the sample mean lunch service time under the new delivery system using the random sample of 44 cars. Write a sentence to interpret the sample mean, using the appropriate number of decimals.

b. Assuming that the new delivery system has no effect on the lunch service times and the population mean is 174.6 seconds, what is the probability of obtaining a sample mean of the time in part a. or less? Include a labelled diagram with the appropriate region shaded in. as part of your solution. Show your work, including all calculations. Write a sentence to interpret your result.

c. Based on your result in part b., do you think that the new delivery system is effective in getting cars through the drive-thru faster? Explain.

d. After presenting your results to the specialist, they have concerns that your result is not valid because the lunch drive-thru service times do not follow a normal distribution. Is your result for part b. valid? Explain.