Question

If the weights of 600 students are normally distributed with a mean of 50 kilograms and a variance of 16 kg

b.) How many students with weights between 50 kgs and 55 kgs. (5 points)

Answer 1

Here the everage weights of 600 students is $50$ kg with standard deviation $\sigma=\sqrt{variance}=4$

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

Then $X$ is normally distributed with mean $50$ kg and standard deviation $4$ kg.

Therefore we have $\mu =50$ and $\sigma=4$  .

Let us take $Z= \frac{X-\mu}{\sigma}$ . Then $Z=\frac{X-50}{4}$.

Now we have to find $P(50<X<55).$

$P(50<X<55)=P(\frac{50-50}{4}<Z<\frac{55-50}{4})$

$=P(0<Z<1.25)$

$=0.8944-0.5=0.3944$

So the number of students with weights between $50$ kg and $55$ kg is $=600*0.3944)=236.64\approx237$