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 Z_0.025 = 1.96)

96

The correct answer is Option (1) → 96

$\text{95\% confidence interval } = (160,170).$

$\text{Half length } E = \frac{170-160}{2} = 5.$

$\sigma = 25.$

$E = z_{0.025}\frac{\sigma}{\sqrt{n}},\; z_{0.025}=1.96.$

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

$\sqrt{n} = \frac{1.96\cdot25}{5} = 9.8.$

$n = 96.04 \approx 96.$