# ISS (Statistical Services) Statistics Paper IV: Questions 20 - 22 of 92

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## Question 20

### Describe in Detail

Essay▾

The following are figures of defective bulbs in 10 lots each containing 30 bulbs. Construct 3-σ control limits for the p-chart.

 Sample No. of defective (d) 1 1 2 3 3 3 4 1 5 0 6 5 7 1 8 1 9 1 10 1

### Explanation

We have n = 30

 Sample No. of defective (d) 1 1 0.033 2 3 0.100 3 3 0.100 4 1 0.033 5 0 0.000 6 5 0.167 7 1 0.033 8 1 0.033 9 1 0.033 10 1 0.033 Total 0.567

Control limits for charts

3-σcontrol limits for the p chart are given by

⇾ 0

… (3 more words) …

## Question 21

### Describe in Detail

Essay▾

Obtain the control limits for for the following data of 25 samples with 4 observations on the basis of volume of the bottles filled.

 Sample No. Observations Sample No. Observations 1 15.85 16.02 15.83 15.93 13 15.85 15.76 15.74 15.98 2 16.12 16.00 15.85 16.01 14 15.73 15.84 15.96 16.10 3 16.00 15.91 15.94 15.83 15 16.20 16.01 16.10 15.89 4 16.20 15.85 15.74 15.93 16 16.12 16.08 15.83 15.94 5 15.74 15.86 16.21 16.10 17 16.01 15.93 15.81 15.68 6 15.94 16.01 16.14 16.03 18 15.78 16.04 16.11 16.12 7 15.75 16.21 16.01 15.86 19 15.84 15.92 16.05 16.12 8 15.82 15.94 16.02 15.94 20 15.92 16.09 16.12 15.93 9 16.04 15.98 15.83 15.98 21 16.11 16.02 16.00 15.88 10 15.64 15.86 15.94 15.89 22 15.98 15.82 15.89 15.89 11 16.11 16.00 16.01 15.82 23 16.05 15.73 15.73 15.93 12 15.72 15.85 16.12 16.15 24 16.01 16.01 15.89 15.86 25 16.08 15.78 15.92 15.98

### Explanation

From the above data we get

From the tables, for n = 4, we have

Control limits for :

And

… (17 more words) …

## Question 22

### Describe in Detail

Essay▾

A electric Company uses a process to paint refrigerators with a coat of enamel. During each shift, a sample of five refrigerators is selected and the thickness of the paint in mm is determined. Find upper control limit (UCL) the lower control limit (LCL) for chart.

 Sample No. Observations 1 2.7 2.3 2.6 2.4 2.7 2 2.6 2.4 2.6 2.3 2.8 3 2.3 2.3 2.4 2.5 2.4 4 2.8 2.3 2.4 2.6 2.7 5 2.6 2.5 2.6 2.1 2.8 6 2.2 2.3 2.7 2.2 2.6 7 2.2 2.6 2.4 2.0 2.3 8 2.8 2.6 2.6 2.7 2.5 9 2.4 2.8 2.4 2.2 2.3 10 2.6 2.3 2.0 2.5 2.4 11 3.1 3.0 3.5 2.8 3.0 12 2.4 2.8 2.2 2.9 2.5 13 2.1 3.2 2.5 2.6 2.8 14 2.2 2.8 2.1 2.2 2.4 15 2.4 3.0 2.5 2.5 2.0 16 3.1 2.6 2.6 2.8 2.1 17 2.9 2.4 2.9 1.3 1.8 18 1.9 1.6 2.6 3.3 3.3 19 2.3 2.6 2.7 2.8 3.2 20 1.8 2.8 2.3 2.0 2.9

### Explanation

From the tables, for n = 5, we have

Control limits for :

And

… (19 more words) …