Question

Assume that the heights of boys in a high school basketball tournament are normally distributed, with mean 70 inches and standard deviation 2.5 inches. What is the expected number of boys in a group of 40 who are taller than 70 inches?

Answer 1

Answer: 20

Step-by-step explanation:

We assume that the heights of boys in a high school basketball tournament are normally distributed.

Given : Mean height of boys : $\mu=70$ inches.

Standard deviation:  $\sigma=2.5$ inches.

Let x denotes the heights of boys in a high school basketball tournament .

Then the probability that a boy is taller than 70 inches will be :-

$P(x> 70)=1-P(x\leq70)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{70-70}{2.5})\\\\=1-P(z\leq0)=1-0.5=0.5\ \ \text{[by using z-value table]}$

Now, the expected number of boys in a group of 40 who are taller than 70 inches will be :-

$40\times0.5=20$

Hence, the expected number of boys in a group of 40 who are taller than 70 inches=20