Among coffee drinkers, men drink a mean of 2.8 cups per day with a standard deviation of 0.5 cups. Assume the number of drinking per day follows a normal distribution.

What proportion drink 3 cups per day or more?

To find the proportion of coffee drinkers who drink 3 cups per day or more, we need to find the area under the normal distribution curve to the right of 3 cups.

To do this, we can standardize the value of 3 cups using the formula:

Z = (X - μ) / σ

Where:
- Z is the standardized value (i.e., the number of standard deviations away from the mean)
- X is the value we want to find the proportion for (in this case, 3 cups per day)
- μ is the mean of coffee drinkers (2.8 cups per day)
- σ is the standard deviation of coffee drinkers (0.5 cups)

Substituting the given values into the formula:

Z = (3 - 2.8) / 0.5 = 0.4 / 0.5 = 0.8

Next, we need to find the proportion (or area) to the right of Z = 0.8. We can use a standard normal distribution table (also known as a Z-table) or a statistical calculator to determine this proportion.

Using a Z-table, we can look up the value for Z = 0.8, which is approximately 0.7881.

This means that the proportion of coffee drinkers who drink 3 cups per day or more is approximately 0.7881 or 78.81%.

Therefore, about 78.81% of coffee drinkers drink 3 cups per day or more.