The random variable $X$ follows normal distribution $f(x)=ce\large\frac{-1/2(x-100)^{2}}{25}$ Then the value of $c$ is

Question

\[\begin{array}{1 1}(1)\sqrt{2\pi}&(2)\frac{1}{\sqrt{2\pi}}\\(3)5\sqrt{2\pi}&(4)\frac{1}{5\sqrt{2\pi}}\end{array}\]

Answer 1

$f(x) =ce^{-\Large\frac{1}{2} \bigg(\frac{(x-\mu)^2}{\sigma}\bigg)}$

Comparing with $f(x) =\large\frac{1}{\sigma \sqrt {2 \pi}}e^{-\Large\frac{1}{2} \bigg(\frac{(x-\mu)^2}{\sigma}\bigg)}$

$\mu=100, \sigma =5$

$e= \large\frac{1}{\sigma \sqrt {2 \pi}}=\frac{1}{5 \sqrt {2 \pi}}$

Hence 4 is the correct answer.