Consider the hot chocolate temperature situation in Exercise 17.9. We found that x̅ and R charts based on subgroups of size 3 for these data are in statistical control with x̅̅ = 140.73 and R̅ = 4.75.

a. Assuming that the hot chocolate temperatures are approximately normally distributed, calculate a range of values that contains almost all (approximately 99.73 percent) of the hot chocolate temperatures.

b. Find reasonable estimates of the maximum and minimum hot chocolate temperatures that would be served at the dining hall.

c. Suppose the dining hall staff has determined that all of the hot chocolate it serves should have a temperature between 130°F and 150°F. Is the process capable of meeting these specifications? Why or why not?

d. Find the sigma level capability of the process.

Data from Exercise 17.9

Explain how the natural tolerance limits compare to the specification limits when

A process is capable of meeting specifications.

A process is not capable of meeting specifications.