Question

Adult male heights have a normal probability distribution with a mean of 70 inches and a standard deviation of 4 inches.

What is the probability that a randomly selected male is more than 74 inches tall?

Answer 1

Answer: 0.1587

Step-by-step explanation:

Given : Adult male heights have a normal probability distribution with a mean of 70 inches and a standard deviation of 4 inches.

i.e. $\mu=70 ,\ \sigma=4$

Let x be the random variable that represents the heights of adult males.

Also, $z=\dfrac{x-\mu}{\sigma}$

For x= 74 , we have

$z=\dfrac{74-70}{4}=1$

Then, the probability that a randomly selected male is more than 74 inches tall:-

$P(x>74)=P(z>1)=1-P(z\leq1)\\\\=1- 0.8413447\\\\=0.1586553\\\\\approx0.1587$ [using z-value table.]

Hence, the probability that a randomly selected male is more than 74 inches tall = 0.1587