Answer to Question #349792 in Statistics and Probability for Meica

Question

The weights(kg) of 11 stem B follow a normal distribution and has a mean of 50 and a standard deviation of 5 how many students have weights greater than 57?

Answer 1

We have a normal distribution with $\mu=50,$ $\sigma=5.$

Let's find the corresponding z-score for $X=57$ :

$z=\frac{X-\mu}{\sigma}=\frac{57-50}{5}=1.4$

So,

$P(X>57)=P(z>1.4)=1-P(z<1.4)=1-0.9192=0.0808.$

As the total number of students is 11 and the probability to have weight greater than 57 is 0.0808,

the number of students of such weight equals:

$11\cdot 0.0808=0.8888\approx1.$

Answer: The number of students that have weights greater than 57 is $\approx1.$