# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 25 - 29 of 165

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## Question number: 25

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2015

### Describe in Detail

Let (X, Y) be distributed as bivariate normal BVN (3, 1, 16, 25, 3/5). Calculate P (4 < Y < 11.84|X=7)

### Explanation

We had known that the conditional distribution of Y given X has mean and variance .

Using conditional mean and variance

## Question number: 26

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2009

### Describe in Detail

A manufacturer of alkaline batteries expects that only 5 % of his products are defective. A random sample of 300 batteries contained 10 defectives. Can we conclude the proportion of defectives in the entire lot is less than 0.5 at 5 % level of significance?

### Explanation

A random sample of 300 batteries contained 10 defectives. A manufacturer of alkaline batteries expects that only 5 % of his products are defective that is testing of hypothesis is

H _{0}: P = 0.05 against H _{1}: P < 0.05

Here n = 300, numbers of defectives… (100 more words) …

## Question number: 27

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2010

### Describe in Detail

You are working as a purchase manager for a company. The following information has been supplied to you by two manufacturers of electric bulbs.

Company A | Company B | |

Mean life | 1300 | 1288 |

Standard deviation | 82 | 93 |

Sample size | 100 | 100 |

Which brand of bulbs are you going to purchase if you desire to take a risk of 5%?

### Explanation

Here the sample size is n = 100

The standard deviation and mean of two samples is different. The null hypothesis is the mean life of bulb of company A is equal to the mean life of bulb of company B and alternative its differ.

The test statistic is… (80 more words) …

## Question number: 28

» Statistical Methods » Measures of Location

Appeared in Year: 2011

### Describe in Detail

Let Z be a random variable with p. d. f. f (z). Let z _{α} be its upper α ^{th} quantile. Show that if X is

a random variable with p. d. f. then σz _{α} +µ is the upper α ^{th} quantile of X.

### Explanation

Let Z be a random variable with p. d. f. f (z). Given that the quantile of z is defined as

X is a random variable with p. d. f. , then quantile is

Assume

Then the limit is

Lower limit is - and upper… (30 more words) …

## Question number: 29

» Probability » Tchebycheffs Inequality

Appeared in Year: 2014

### Describe in Detail

Show that for 40, 000 throws of a balanced coin, the probability is at least 0.99 that the proportion of heads will fall between 0.475 and 0.525.

### Explanation

For balanced coin the probability is p = 0.5. For Bernoulli trails where n = 40, 000, the mean and standard deviation is

Using Chebyshev’s inequality,

The question says that the probability is at least 0.99 that is

So, the number of heads comes between… (34 more words) …