Question

Heights of men in the United States approximately normally distributed with a mean of 70 inches and a standard deviation of 2.5 inches. What is the probability that randomly selected men will be taller than 75 inches

Answer 1

0.0228

Explanation:

Given that
`\mu=70, \sigma=2.5`

-Let X be the height of the randomly selected man.

-The probability that X>75 inches is calculated as:

`P(X>75)=P(z>(X-\mu)/(\sigma))\\\\=P(z>(75-70)/(2.5))\\\\=P(z>2)\\\\\therefore P(X>75)=1-P(X<75)\\\\=1-0.97725\\\\=0.0228`

Hence, the probability that a random pick is taller than 75 inches is 0.0228