Question

Exercise 2: Canned Tomatoes During long production runs of canned tomatoes, the average weights (in mL) of samples of five cans of standard-grade tomatoes in puree form were taken at 30 control points during an 11-day period. These results are shown in the dataset Tomatoes.xls. When the machine is performing normally, the average weight per can is 621mL with a standard deviation of 35.5mL. 1. Using SPSS, plot the chart. 2. How many sample means falls outside the control interval? Explain! 3. If we suppose that the samples are independents, what is the probability that the process is in control?

Sample Number	Average Weight
1	654.9
2	603.8
3	623.7
4	606.7
5	618
6	584
7	569.8
8	606.7
9	609.5
10	572.7
11	575.5
12	569.8
13	615.2
14	595.3
15	612.3
16	606.7
17	578.3
18	646.4
19	598.2
20	586.8
21	612.3
22	635
23	603.8
24	598.2
25	569.8
26	601
27	64.2
28	598.2
29	612.3
30	603.8

Answer 1

Sol:

1).

The plot using SPSS is:

Control Chart: Weight 1,200 Weight UCL = 741.6130 - Average = 584.4300 LCL = 4272470 Rule violation No Yes 1,000 008 600 400 200 0 7.00 9.00 11.00 13.00 15.00 17.00 19.00 21.00 23.00 25.00 27.00 29.00 Sigma level:

2).

There is one sample mean that falls outside the control interval at sample number 27.

3).

z = (584.43 - 621)/35.5 = -1.03

P (z = -1.03) = 0.1515

The probability that the process is in control is 0.1515.

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