Question

The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that an 18-year-old man selected at random is greater than 65 inches tall? Round your answer to four decimal places.

Answer 1

The probability that an 18-year-old man selected at random is greater than 65 inches tall is 0.8413.

Explanation:

We are given that the heights of 18-year-old men are approximately normally distributed with mean 68 inches and a standard deviation of 3 inches.

Let X = heights of 18-year-old men.

So, X ~ Normal(
`\mu=68,\sigma^(2) =3^(2)`)

The z-score probability distribution for the normal distribution is given by;

Z =
`(X-\mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = mean height = 68 inches

`\sigma` = standard deviation = 3 inches

Now, the probability that an 18-year-old man selected at random is greater than 65 inches tall is given by = P(X > 65 inches)

P(X > 65 inches) = P(
`(X-\mu)/(\sigma)` >
`(65-68)/(3)` ) = P(Z > -1) = P(Z < 1)

= 0.8413

The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.8413.