A student wants to estimate the mean of population for some sample. The probability is 0.95 that sample mean will not differ by true mean by more than 50% of standard deviation. $(Z_{0.025}=1.96)$. The size of sample taken by student is :

15

The correct answer is Option (2) → 15

Margin of error = $Z_{α/2}×\frac{σ}{\sqrt{n}}$

$⇒0.5σ=1.96×\frac{σ}{\sqrt{n}}$

$⇒n=\frac{3.8416}{0.25}≃15$