Statistics & Applications

Inferential

Medium

applied

Which of the following are true ?

(A) If the mean of a normal variate is 12 and standard deviation is 4, then the Z-score of data point 20 is 2.

(B) Mean of the numbers obtained on throwing a die having '1' on three faces, '2' on two faces and '5' on one face is 3.

(C) If the variance of a Poisson's distribution is 2, then $P(X=0)=\frac{1}{e^2}$ .

(D) For a binomial distribution, mean = 9 and the standard deviation is $\frac{3}{2}$ , then the number of trials is 12.

Choose the correct answer from the options given below:

(A), (B) and (D) only

(A), (B) and (C) only

(B), (C) and (D) only

(A), (C) and (D) only

✅ Correct Option: 4

(A): $z=\frac{20-12}{4}=2$ , true. (C): variance $2$ gives $\lambda=2$ , so $P(X=0)=e^{-2}$ , true. (D): $np=9$ and $npq=\frac{9}{4}$ give $q=\frac{1}{4}$ , $p=\frac{3}{4}$ and $n=12$ , true.

(B) is false, since the mean is $\frac{3(1)+2(2)+1(5)}{6}=2$ , not $3$ .

2026: 26 May Shift 2

Match the terms mentioned List I with the definitions mentioned in List II.

LIST-I	LIST-II
A. Confidence interval	I. In a hypothesis test, the probability of making wrong decision when the null hypothesis is true.
B. Margin of error	II. The number of independent pieces of information on which an approximation is based.
C. Significance level	III. A range of values, derived from sample statistic which is likely to contain the value of an unknown population parameter.
D. Degree of freedom	IV. In a confidence interval, the range of values, above and below the sample statistic.

Choose the correct answer from the options given below:

2026: 31 May Shift 2

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	The measurable characteristic of a population is called	I. Statistic
B.	The measurable characteristic of a sample is called	II. Sample size
C.	The number of objects in a sample is called	III. Null hypothesis
D.	A tentative assumption about population	IV. Parameter

Choose the correct answer from the options given below:

2026: 25 May Shift 1

The value of t-statistic for the following data as Population mean is 51, Sample mean is 54, Sample size is 10 and sample variance is 36, is:

2025: 21 May Shift 1

Which of the following are correct?

(A) The probability curve in t-distribution is symmetric about the line t=0.

(B) t-axis is an asymptote of the curve.

(D) As the number of degrees of freedom increases, the t-distribution curve moves closer to the binomial distribution.

Choose the correct answer from the options given below:

2026: 19 May Shift 1

Match List-I with List-II

List-I	List-II
(A) It describes the accuracy of a sampling method.	(I) Confidence interval
(B) It describes the uncertainity of a sampling method.	(II) Hypothesis
(C) It is used to express the precision and uncertainity of a sampling process.	(III) Margin of error
(D) An educated guess which needs to be tested.	(IV) Confidence level

Choose the correct answer from the options given below:

2026: 31 May Shift 2

Consider the following hypothesis test :

$H_0: \mu \le 35$

$H_a: \mu > 35$

A sample of 49 provided a sample mean of 38.2 The population standard deviation is 8. The value of test-statistic is,

Solution

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