# 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

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## 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

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## 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

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## 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

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## 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

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