A 95% confidence interval for a population mean was reported to be 152 to 160. If standard deviation $σ = 15$, Then the sample size is: ($Z_{.025}=1.96$)

54

The correct answer is Option (3) → 54 **

95% confidence interval: $152$ to $160$

Mean $=156$ and margin of error:

$E = 160 - 156 = 4$

Formula for confidence interval margin:

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

Substitute values:

$4 = 1.96\,\frac{15}{\sqrt{n}}$

Solve for $n$:

$\sqrt{n} = 1.96 \cdot \frac{15}{4}$

$\sqrt{n} = 1.96 \cdot 3.75 = 7.35$

$n = 7.35^{2} \approx 54.02$

Sample size ≈ 54