Answer:
The probability that an 18-year-old man selected at random is greater than 65 inches tall is 0.8413.
Step-by-step 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([tex]\mu=68,\sigma^{2} =3^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean height = 68 inches
[tex]\sigma[/tex] = 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( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{65-68}{3}[/tex] ) = 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.
