Question

Assume the height of soldiers follows the Normal Distribution with miean 68 and variance 25". In a reg1unent of 1000 soldiers, how any are expected to be (1) over ô feet tall (n) under S feet o inches and (i) exactly 65 inches tall?​

Answer 1

Answer: Number of soldiers in a regiment = 363.

Explanation:the The mean height of soldiers = 68.22 inches

The variance of soldiers = 10.8

We need to calculate

P(\text{ over 6 feet})=P(\text{ over 72 inches })=P(Z > 72)P( over 6 feet)=P( over 72 inches )=P(Z>72)

Using the formula for normal distribution,

\begin{gathered}P(Z > \frac{X-\mu}{\sigma})\\\\=P(Z > \frac{72-68.22}{10.8})\\\\=P(Z > 0.35)\end{gathered}P(Z>σX−μ)=P(Z>10.872−68.22)=P(Z>0.35)

Using the normal distribution table ,we get,

P(Z > 0.35)=1-0.63683=0.36318P(Z>0.35)=1−0.63683=0.36318

So,

\text{ Number of soldiers in a regiment }=1000\times 0.36318=363.18 Number of soldiers in a regiment =1000×0.36318=363.18

So, Number of soldiers in a regiment = 363 approx.