Basketballs. A company that makes basketballs has the motto: “Our basketballs are ready to play.” Therefore, it is important to the company that the basketballs are inf lated with the proper amount of air when shipped.

Most basketballs are inf lated to 7 to 9 pounds per square inch. From a set of calibration data, the following statistics were measured:

X = 8.05 R = 0.65 Recently the company selected a random basketball from its production line at four different time periods over its normal production day. The results were recorded and listed in the following table.

8:00–10:00 am 10:00 am Noon–2:00 pm 2:00–4:00 Day 1 8.05 8.49 7.59 7.90 Day 2 8.16 7.62 7.71 7.90 Day 3 8.30 8.07 8.14 8.12 Day 4 7.55 8.82 8.12 8.18 Day 5 8.18 7.76 7.70 7.65 Day 6 7.88 7.90 7.99 7.62 Day 7 8.01 8.02 7.32 8.10 Day 8 8.32 7.89 8.62 7.89 Day 9 7.94 7.75 7.58 7.74 Day 10 7.38 7.47 7.93 7.73 Day 11 7.44 7.84 7.87 8.33 Day 12 8.30 8.04 7.94 8.09 Day 13 8.46 8.20 7.93 7.89 Day 14 8.10 8.38 8.08 7.80 Day 15 7.70 7.68 8.25 8.40 Day 16 8.32 7.98 7.65 8.32 Day 17 8.13 7.96 8.21 8.51 Day 18 7.69 8.07 7.55 8.26 Day 19 7.86 8.55 8.05 7.63 Day 20 7.97 8.08 7.89 7.97 Day 21 8.73 7.84 7.94 8.07 Day 22 8.14 7.56 7.97 7.86 Day 23 7.64 7.89 7.47 7.66 Day 24 8.33 7.87 7.89 7.62 Day 25 8.00 7.61 7.65 7.39 Day 26 7.31 8.66 7.71 7.29 Day 27 7.58 7.95 8.13 8.52 Day 28 7.91 8.53 7.86 7.96 Day 29 8.34 8.10 8.45 8.16 Day 30 8.04 8.25 7.13 8.12

a) Create an X chart based on the calibration data statistics for these 30 samples.

b) Create an R chart based on the calibration data statistics for these 30 samples.

c) Assuming that the process was in control during the calibration period, is the company’s process for filling its basketball with the proper amount of air in control?