The normal distribution is called as standard normal distribution when Option 1: Mean () = 1 and standard deviation () = 0 for a data set Option 2: Mean () = 1 and standard deviation () = 1 for a data set Option 3: Mean () = 0 and standard deviation () = 1 for a data set Option 4: Mean () = 0 and standard deviation () = 0 for a data set

Answer: Mean () = 0 and standard deviation () = 1 for a data set. Solution: The standardised variable Z = (X-)/() has mean 0 and standard deviation 1. A normal distribution with these parameters is called the standard normal distribution.

Statistics & Applications

Inferential

Easy

applied

The normal distribution is called as standard normal distribution when

Mean ( $\mu$ ) = 1 and standard deviation ( $\sigma$ ) = 0 for a data set

Mean ( $\mu$ ) = 1 and standard deviation ( $\sigma$ ) = 1 for a data set

Mean ( $\mu$ ) = 0 and standard deviation ( $\sigma$ ) = 1 for a data set

Mean ( $\mu$ ) = 0 and standard deviation ( $\sigma$ ) = 0 for a data set

✅ Correct Option: 3

The standardised variable $Z = \dfrac{X-\mu}{\sigma}$ has mean $0$ and standard deviation $1$ .

A normal distribution with these parameters is called the standard normal distribution.

2026: 21 May Shift 1

As per the concept of inferential statistics, population stands for:-

2025: 16 May Shift 1

Which of the following are correct?

(A) A statistical hypothesis is a statement about the population parameter which may be true or false.

(B) In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false.

(C) In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true.

(D) The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic.

Choose the correct answer from the options given below:

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A 95% confidence interval for a population mean was reported to be 152 to 160. If sample standard deviation $\sigma=15$ , then sample size used in this study is (Given $Z_{0.025}=1.96$ )

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Which of the following are the assumptions underlying the use of t-distribution?

(A) The variance of population is known.

(B) The samples are drawn from a normally distributed population.

(D) It depends on a parameter known as degree of freedom.

Choose the correct answer from the options given below:

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If we reject the null hypothesis when it is true, we might be making

2025: 13 May Shift 2

When the two independent small samples of sizes $n_1$ and $n_2$ with means $\bar{x}_1$ and $\bar{x}_2$ respectively are drawn from populations with identical population variances, the test-statistic is computed as

The normal distribution is called as standard normal distribution when

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