Assume that the life expectancy of U.S. males is normally distributed with a mean of 80 years and a standard deviation of 4 years. What is the probability that a randomly selected male will live more than 85 years?

It depends on when the male is selected. If at birth, then you can use the normal distribution, mean above, with std deviation 4, and you see 85 is just slightly over one standard deviation.

But if the male is selected after birth, it changes, and you need to think on that. For instance, what if the male is now 90? 84? 50? Those gents will have a probablity greater than if chosen at birth.

Z = (x - μ)/SD = (85 - 80)/4 = 1.25

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score.

If the man is now 90, the probability = 1 (certainty).

which of of the following stateements are correct?

a. A normal distribution is any distribution that is not normal
b. the graph of a normal distribution is bell-shaped
c. If a population has a normal distribution, the mean and the median are not equal
d. The graph of a normal distribution is symmetric

To find the probability that a randomly selected male will live more than 85 years, we need to calculate the z-score for 85 years using the given mean and standard deviation.

The z-score formula is:

z = (x - μ) / σ

where:
- x is the value we want to find the z-score for (85 years in this case),
- μ is the mean (80 years),
- σ is the standard deviation (4 years).

Substituting the values into the formula, we have:

z = (85 - 80) / 4
= 5 / 4
= 1.25

Now, we need to find the probability of a z-score greater than 1.25. We can use the standard normal distribution table or a calculator to find this probability.

Using the standard normal distribution table, the probability associated with a z-score of 1.25 is approximately 0.8944. However, since we are interested in the probability of a value greater than 85 years, we need to subtract this probability from 1 to obtain the probability of the value being greater than 85.

P(X > 85) = 1 - 0.8944
= 0.1056

Therefore, the probability that a randomly selected male will live more than 85 years is approximately 0.1056, or 10.56%.