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

Access detailed explanations (illustrated with images and videos) to 92 questions. Access all new questions- tracking exam pattern and syllabus. View the complete topic-wise distribution of questions. Unlimited Access, Unlimited Time, on Unlimited Devices!

View Sample Explanation or View Features.

Rs. 350.00 -OR-

## 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

… (2 more words) …

## 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&#8230;

… (32 more words) …

## Question 29

Edit

### 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

… (3 more words) …

## 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

… (20 more words) …