# ISS (Statistical Services) Statistics Paper IV: Questions 23 - 26 of 92

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## Question 23

### Describe in Detail

Essay▾A machine is manufacturing mica discs. Samples of size 5 are drawn every hour and their thickness in units are recorded as follows. On the basis of chart, Check whether the production is under control?

Sample No. | Observations | ||||

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

From the tables, for n = 5, we have

**Control limits for** :

And

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## Question 24

### Explanation

## Kings Method

An abridged life table consists of all columns of a life table for ages distant apart usually 5 to 10 years or for age groups usually of width 5 to 10 years. In this way there is tremendous cut in size of life-tables, and hence such life tables are named as abridged life table.

Central mortality rate can be calculated precisely provided …

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## Question 25

### Describe in Detail

Essay▾a) If the average range for the 4 samples is 0.2 millimeters and the average mean of the observations is 12.5 millimeters, obtain the three-sigma control limits for the sample mean.

b) 5 observations have been taken from the 10 samples in order to test the volume in the bags. The average sample range is 0.5 ounces. Obtain the 3-σ limits for the sample range.

### Explanation

a) It is given that n = 5 and

Based on tables for control charts. For n = 5, The value of

Control limits for :

And

b) We are given that, number of observations, n = 5,

For n = 5, from the tables we have,

**Control limits for R chart**:

= 0

Full control chart constants are available at examrace. com

## Question 26

### Describe in Detail

Essay▾A new oven has been installed in a bakery and to test the efficiency of this, the oven temperature readings have been taken at four different places inside the oven every 30 min. The following table gives readings. Determine the control limits for the mean temperature.

Time | Readings | |||

8: 00 | 400 | 500 | 550 | 390 |

8: 30 | 440 | 420 | 380 | 380 |

9: 00 | 410 | 450 | 470 | 430 |

9: 30 | 390 | 390 | 410 | 410 |

10: 00 | 370 | 420 | 460 | 410 |

10: 30 | 390 | 400 | 390 | 400 |

### Explanation

From the tables, for n = 6, we have

**Control limits for** :

And

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