Question

Mean height of 100 Students is 150 cms and the standard deviation is 15 cms. Assuming that the height are

normally distributed, find how many students have height between 110 to 165 cms.

Answer 1

Let $X=$ student's height: $X\sim N(\mu, \sigma^2).$

Given $\mu=150cm, \sigma=15cm.$

$$P(110<X<165)=P(X<165)-P(X\le110)$$

$$=P(Z<\dfrac{165-150}{15})-P(Z\le\dfrac{110-150}{15})$$

$$=P(Z<1)-P(Z\le-\dfrac{8}{3})$$

$$\approx0.8413447-0.0038304\approx0.837514$$

$$0.837514(100)=84$$

84 students have height between 110 to 165 cm.