CUET CUET Mathematics 2024 - If 95 \% confidence interval for the population mean was reported to be 160 to 170 and =25, then size of the sample used in this study is: (Given Z_0.025=1.96 ) | PYQs + Solutions

CUET Mathematics 2024

Statistics & Applications

Inferential

Medium

If $95 \%$ confidence interval for the population mean was reported to be $160$ to $170$ and $\sigma=25$ , then size of the sample used in this study is: (Given $\mathrm{Z}_{0.025}=1.96$ )

96

125

54

81

Correct Option: 1

For a confidence interval with known standard deviation:

\text{Half-width} = z_{\alpha/2} \cdot \dfrac{\sigma}{\sqrt{n}}

Given:

\newline

- Half-width

= (170 - 160)/2 = 5

\newline

z_{0.025} = 1.96

\newline

\sigma = 25

Plugging these values into the formula:

5 = 1.96 \cdot \frac{25}{\sqrt{n}}

\sqrt{n} = \frac{1.96 \cdot 25}{5}

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

n = \left(\frac{49}{5}\right)^2 = \frac{2401}{25} = 96.04

Therefore, the closest answer is 96.