Question

800 students have a mean weight of 75 kg and standard deviation of 5kg. How many students weigh more than 80 kg

Answer 1

Let $X$ be a random variable such that weight of the students, which is normally distributed with mean $75$ kg and standard deviation $5$ kg.

Then we have $\mu=75$ and $\sigma =5$

Let us consider $Z=\frac{X-\mu}{\sigma }$. Then $Z=\frac{X-75}{5}$

Now we have to find $P(X>80)$

$\therefore P(X>80)=P(Z>\frac{80-75}{5})=P(Z>1)=0.5-P(0<Z<1)$

$=0.5-0.3413$ $[P(0<Z<1)=0.3413$ from normal distribution table $]$ $=0.1587$

$\therefore$ Number of students having weight more than $80$ kg is $=80×P(X>80)$

$=80×0.1587$

$=127$ (approximately)

Which is the required answer.