ANSWER (B) AND (C) PLAESE

Q2) At Zoom Zone, kids will have a guided fun tour, and enjoy ice-cream at the end of the tour. Service quality control at Zoom Zone requires that the length of the tour is between 30 and 50 minutes, and one serving of ice-cream is between 2.75 and 3.25 ounces. Any cases beyond either the tour time or ice-cream weight tolerances would be considered as service defects. The management aims for a defect rate of no more than 1 out of 20. A current report indicates that the average tour time is 40 minutes with a standard deviation of 8 minutes, and the ice-cream weight per serving is has a mean of 3.00 ounces with a standard deviation of 0.10 ounces. The management estimates that improving the ice-cream step would require weighing each scoop and causing much longer waiting time for kids. However, an improvement in tour time is possible through reducing the process variability. To find how much reduction in the tour time variability is required, consider the following steps in sequence: A) What is the probability that the ice-cream step is not defective? Briefly justify.

B) Assume the variabilities in the two steps are independent. To achieve the desired quality standard, what should be the probability that the tour step is not defective?

C) What should be the standard deviation of the tour time to bring Zoom Zone up to the desired service quality level? Briefly justify. (You may use the closest probability in the z-table. If you think your answer to the previous two parts might be incorrect, please state your logic clearly here to get partial credits. Otherwise, showing calculations suffices.)