Question

the mean height of soldiers is 68.22 inches with a variance of 10.8. Assuming the distribution of heights to be normal, how many soldiers in a regiment of 1000 would you expect to be over 6 feet tall? 

Answer 1

Answer: Number of soldiers in a regiment = 363.

Explanation:

Since we have given that

The mean height of soldiers = 68.22 inches

The variance of soldiers = 10.8

We need to calculate

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

Using the formula for normal distribution,

$P(Z> \frac{X-\mu}{\sigma})\\\\=P(Z>\frac{72-68.22}{10.8})\\\\=P(Z>0.35)$

Using the normal distribution table ,we get,

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

So,

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

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

Answer 2

Answer:

Step-by-step explanation: