Assume that the heights of men are normally distributed with a mean of 70.7 inches and a standard deviationof 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean height greater than71.7 inches.
A) 0.0021
B) 0.0210
C) 0.9005
D) 0.9979

Question

Quizplus · Accepted Answer

To find the probability that the mean height of 64 randomly selected men is greater than 71.7 inches, we use the formula for the standard error of the mean: $SE = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. Here, $\sigma = 2.8$ inches and $n = 64$, so $SE = \frac{2.8}{\sqrt{64}} = \frac{2.8}{8} = 0.35$ inches. We then calculate the z-score for a mean height of 71.7 inches: $z = \frac{71.7 - 70.7}{0.35} = \frac{1}{0.35} \approx 2.857$. Looking up this z-score in a standard normal distribution table or using a calculator gives a probability of about 0.9979 that a z-score is less than 2.857, so the probability of it being greater is $1 - 0.9979 = 0.0021$.

Assume That the Heights of Men Are Normally Distributed with a Mean