# ISS (Statistical Services) Statistics Paper IV: Questions 27 - 30 of 92

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## Question 27

### Describe in Detail

Essay▾Compute GFR, SFR, TFR and GRR from the data given below:

Age groups of child bearing females | Number of women (՚000) | Total births |

15 - 19 | 16.0 | 260 |

20 - 24 | 16.4 | 2244 |

25 - 29 | 15.8 | 1894 |

30 - 34 | 15.2 | 1320 |

35 - 39 | 14.8 | 916 |

40 - 44 | 15.0 | 280 |

45 - 49 | 14.5 | 145 |

Assume that the proportion of female births is 46.2 percent.

### Explanation

First write the formula of GFR, SFR, TFR and GRR is

Age groups of child bearing females | Number of women (՚000) | Total births | ASFR |

15 - 19 | 16 | 260 | 16 |

20 - 24 | 16.4 | 2244 | 137 |

25 - 29 | 15.8 | 1894 | 120 |

30 - 34 | 15.2 | 1320 | 87 |

35 - 39 | 14.8 | 916 | 62 |

40 - 44 | 15 | 280 | 19 |

45 - 49 | 14.5 | 145 | 10 |

Total | 107.7 | 7059 | 451 |

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## Question 28

### Describe in Detail

Essay▾The following are the figures of defectives in 22 lots each containing 2,000 bulbs. Ind control limit for p-Chart.

425 | 430 | 216 | 341 | 225 | 322 | 280 | 306 | 337 | 305 | 356 |

402 | 216 | 264 | 126 | 409 | 193 | 326 | 280 | 389 | 451 | 420 |

### Explanation

**We have n = 2000**

S. No. | d | |

1 | 425 | 0.2125 |

2 | 430 | 0.215 |

3 | 216 | 0.108 |

4 | 341 | 0.1705 |

5 | 225 | 0.1125 |

6 | 322 | 0.161 |

7 | 280 | 0.14 |

8 | 306 | 0.153 |

9 | 337 | 0.1685 |

10 | 305 | 0.1525 |

11 | 356 | 0.178 |

12 | 402 | 0.201 |

13 | 216 | 0.108 |

14 | 264 | 0.132 |

15 | 126 | 0.063 |

16 | 409 | 0.2045 |

17 | 193 | 0.0965 |

18 | 326 | 0.163 |

19 | 280 | 0.14 |

20 | 389 | 0.1945 |

21 | 451 | 0.2255 |

22 | 420 | 0.21 |

Total | 3.5095 |

**Control limits for** **charts**

3-σcontrol limits…

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## Question 29

### Describe in Detail

Essay▾Each day a sample of 1500 items from a production process was examined. The number of defectives found in each sample was as follows. With a suitable control chart, check out for control 4, 6, 6, 2,15, 4,4

### Explanation

We have n = 30

S. No. | d | |

1 | 4 | 0.00267 |

2 | 6 | 0.00400 |

3 | 6 | 0.00400 |

4 | 2 | 0.00133 |

5 | 15 | 0.01000 |

6 | 4 | 0.00267 |

7 | 4 | 0.00267 |

Total | 41 | 0.02733 |

**Control limits for** **charts**

3-σ control limits for the p chart are given by

⇾ 0

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## Question 30

### Describe in Detail

Essay▾a) The number of customer complaints are recorded at a television manufacturing company. Complaints have been recorded over the past 20 weeks. Construct 3-σ control limits for the *c*-chart.

Week | No. of complaints | Week | No. of complaints |

1 | 0 | 11 | 4 |

2 | 3 | 12 | 3 |

3 | 4 | 13 | 1 |

4 | 1 | 14 | 1 |

5 | 0 | 15 | 1 |

6 | 0 | 16 | 0 |

7 | 3 | 17 | 2 |

8 | 1 | 18 | 1 |

9 | 1 | 19 | 2 |

10 | 0 | 20 | 2 |

b) A machine is manufacturing mica discs. samples of size 5 are drawn every hour and their thickness in units are recorded as follows. From this data construct 3-σ control limits for **chart**.

Sample No. | Observstions | ||||

1 | 8 | 9 | 15 | 4 | 11 |

2 | 7 | 10 | 7 | 6 | 8 |

3 | 11 | 12 | 10 | 9 | 10 |

4 | 12 | 8 | 6 | 9 | 12 |

5 | 11 | 10 | 6 | 14 | 11 |

6 | 7 | 7 | 10 | 4 | 11 |

7 | 10 | 7 | 4 | 10 | 10 |

8 | 8 | 11 | 11 | 7 | 7 |

9 | 8 | 11 | 8 | 14 | 12 |

10 | 12 | 9 | 12 | 17 | 11 |

11 | 7 | 7 | 9 | 17 | 13 |

12 | 9 | 9 | 4 | 4 | 11 |

13 | 10 | 12 | 12 | 12 | 12 |

14 | 8 | 11 | 9 | 6 | 8 |

15 | 10 | 13 | 9 | 4 | 9 |

16 | 9 | 11 | 8 | 5 | 11 |

### Explanation

a) Average number of defects per sample is

= 1.5 + = 1.5 + 3 (1.22) = 5.174

= ⇾ 0

Since number of defects cannot be negative, can be considered as zero. (rounded up to zero)

b) Second question:

From the tables, for n = 5, we have

**Control limits for** :

And

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