# ISS (Statistical Services) Statistics Paper IV: Questions 1 - 5 of 92

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## Question number: 1

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Explain stationary and stable population. State the situation when the age distribution of two stable populations would be identical.

### Explanation

Stationary Population: If the size of a population is constant and its composition according to age and sex also remains constant over time, then such a population is known as stationary population. The constancy in population for size and composition is maintained if,

1. Births and deaths are equal in number and are uniformly distributed over the year

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## Question number: 2

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Discuss the main sources of demographic data in the Indian system. Give your suggestion for the measures to improve the quality of data.

### Explanation

The main sources of demographic data in India are:

(i) Census: The most important source of demographic data in India is the census. It provides valuable information about the country and its people at a given point of time. A population census is an official enumeration of the inhabitants of a country with statistics relating to their location, age

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## Question number: 3

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Explain briefly the uses of life table

### Explanation

A life table mainly displays the death rate between two consecutive birth days and expectation of life at any age of a cohort. The information revealed by a life-table has application in many fields and hence its uses can be summarized as given below:

1. Life tables are of great use to actuaries to estimate the insurance risks and premiums.

2. Life tables

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## Question number: 4

» Operations Research and Reliability » Queuing Models » M/M/1 Model

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

(d) Show that for M/M/1/∞ queue model

where λn and µn are the means of Poisson and exponential distributions respectively where there are n people in the system.

### Explanation

Suppose the system is in state j at time t. There are j people in the system. In the next time interval of a very small duration Δt, the system can move to state j-1or j + 1with the following probabilities:

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## Question number: 5

» Statistical Quality Control » Control Charts » Variable

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Essay Question▾

### Describe in Detail

Following is the data of 25 samples with 4 observations on the basis of volume of the bottles filled. Using a control limits for chart, test whether the production is under control?

 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 :

=0

Since the sample points fall within

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