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: 20Step-by-step explanation:We assume that the heights of boys in a high school basketball tournament are normally distributed.Given : Mean height of boys : [tex]\mu=70[/tex] inches. Standard deviation:  [tex]\sigma=2.5[/tex] 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 :-[tex]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]}[/tex]Now, the expected number of boys in a group of 40 who are taller than 70 inches will be :-[tex]40\times0.5=20[/tex]Hence, the expected number of boys in a group of 40 who are taller than 70 inches=20