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

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

96

The correct answer is Option (3) → 96

Given:

Confidence interval: 140 to 150

Population standard deviation: σ = 25

95% confidence interval → Z₀.₀₂₅ = 1.96

Confidence interval formula:

$\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$

Margin of error (E) = (150 - 140)/2 = 5

$E = Z \frac{\sigma}{\sqrt{n}}$

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

$\sqrt{n} = \frac{1.96 × 25}{5}$

$\sqrt{n} = \frac{49}{5} = 9.8$

$n = (9.8)^2 \approx 96.04$

Sample size n ≈ 96