Question

The weights of 1,000 children average is 50 kg and the standard deviation is 5 kg. How many children weigh between 40 kg and 55 kg?

Answer 1

Here the everage weights of the $1000$ children is $50$ kg with standard deviation $5$ kg.

Let $X$ be a random variable denotes the weight of the students.

Then $X$ is normally distributed with mean $50$ kg and standard deviation $5$ kg.

Therefore we have $\mu =50$ and $\sigma=5$ .

Let us take $Z= \frac{X-\mu}{\sigma}$ . Then $Z=\frac{X-50}{5}$.

Now we have to find $P(40<X<55).$

$\therefore P(40<X<55)=P(\frac{40-50}{5}<Z<\frac{55-50}{5})$

$=P(-2<Z<1)$

$=P(0< Z< 2)+P(0< Z< 1)$

$=0.4772+0.3413$ [ from normal distribution table ]

$=0.8185$

So the number of children weight between $40$ kg and $55$ kg is $=(1000×0.8185)=819$ (approximately)