The heights of South African men are normally distributed with a mean of 64 inches and a standard deviation of 2 inches.

a) What is the probability that a randomly selected woman is taller than 66 inches?

To find the probability that a randomly selected woman from South Africa is taller than 66 inches, we can use the concept of the standard normal distribution.

The first step is to standardize the value 66 inches using the formula z = (x - μ) / σ, where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, x = 66 inches, μ = 64 inches, and σ = 2 inches. Plugging these values into the formula, we get z = (66 - 64) / 2 = 1.

Next, we need to find the area under the standard normal distribution curve to the right of z = 1. This represents the probability that a randomly selected woman's height is taller than 66 inches.

Using a standard normal distribution table or a statistical software, we can find that the area to the right of z = 1 is approximately 0.1587.

Therefore, the probability that a randomly selected woman from South Africa is taller than 66 inches is approximately 0.1587 or 15.87%.