Statistics & Applications

Inferential

Medium

applied

If 95% confidence interval for the population mean was reported to be 140 to 150 and $\sigma = 25$ , then size of the sample used in this study is:

[Given: $Z_{0.025} = 1.96$ ]

120

112

✅ Correct Option: 3

The confidence interval is 140 to 150, with $\sigma = 25$ and $Z_{0.025} = 1.96$ .

The sample mean is the midpoint of the confidence interval:

$\bar{x} = \frac{140 + 150}{2}$

$\bar{x} = \frac{290}{2}$

$\bar{x} = 145$

The margin of error is the distance from the mean to either endpoint:

$E = 150 - 145 = 5$

The margin of error formula for a confidence interval is:

$E = Z_{\alpha/2} \times \frac{\sigma}{\sqrt{n}}$

Substituting the known values:

$5 = 1.96 \times \frac{25}{\sqrt{n}}$

$5 = \frac{49}{\sqrt{n}}$

$5\sqrt{n} = 49$

$\sqrt{n} = \frac{49}{5}$

$\sqrt{n} = 9.8$

$n = (9.8)^2$

$n = 96.04$

$n \approx 96$

Therefore, the sample size used in this study is 96.

2026: 30 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Snowball sampling	(I) Statistic
(B) A measurable characteristic of a sample	(II) Parameter
(C) Stratified sampling	(III) Non-probability sampling
(D) A measurable characteristic of a population	(IV) Probability sampling

Choose the correct answer from the options given below:

2025: 13 May Shift 2

Which of the following is NOT correct about the Central Limit Theorem?

2025: 26 May Shift 2

With reference to sampling, which of the following are correct?

(A) Simple random sampling is probability sampling

(B) Snow-ball sampling is non-probability sampling

(D) Cluster sampling is non-probability sampling

Choose the correct answer from the options given below:

2025: 2 June Shift 1

A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150. If the population mean is 56 then the value of t-test statistic is:

2025: 16 May Shift 1

The point estimate of the population standard deviation for the random sample 5, 8, 10, 7, 10, 14 is:

2026: 25 May Shift 1

A simple random sample of 49 items from a population with standard deviation 10 resulted in a sample mean of 25. Then the 95% confidence interval for population mean are :

(Given $z_{\alpha/2} = 1.96$ where $\alpha = 0.05$ )

If 95% confidence interval for the population mean was reported to be 140 to 150 and σ=25\sigma = 25σ=25, then size of the sample used in this study is: [Given: Z0.025=1.96Z_{0.025} = 1.96Z0.025​=1.96]

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If 95% confidence interval for the population mean was reported to be 140 to 150 and $\sigma = 25$ , then size of the sample used in this study is:

[Given: $Z_{0.025} = 1.96$ ]