Question: A manufacturing process fills boxes of cereal. The nominal net weight per box is 16 ounces. We wish to establish control limits for the filling process by drawing a random sample of 5 boxes each hour during 24 hours of operation. The deviations (above and below the mean) of each box sample is as shown:

Deviations in hundredths Deviations in hundredths

Sample X₁ X₂ X₃ X₄ X₅ Sample X₁ X₂ X₃ X₄ X₅

1 9 -60 32 -15 99 13 -45 -23 90 -39 55

2 -54 -19 -7 -10 7 14 68 -56 -80 -37 -80

3 42 -47 52 50 -24 15 -59 -15 28 11 10

4 -1 55 89 45 -63 16 -48 86 50 -75 72

5 80 48 -64 -27 67 17 12 8 -51 -47 -74

6 6 -52 -37 -89 80 18 35 -18 -46 16 76

7 -6 49 15 -34 -20 19 -91 95 -72 -24 -82

8 -26 54 7 -20 31 20 -89 -75 -10 -94 4

9 -57 -96 -57 -24 3 21 -49 63 25 38 -31

10 -79 -80 5 5 69 22 33 2 22 -96 -23

11 52 5 -32 89 -30 23 10 17 47 14 93

12 -80 17 -52 -42 66 24 55 -66 94 -55 42

a. Construct an X-bar control chart from these data.

b. Construct an R-chart from these data.

c. Perform a “runs-test” on this data.

d. Is the process in control?