The heights of women at a large university are approximately bell-shaped, with a mean of 65 inches and standard deviation of 2.5 inches. What is the probability that two randomly selected women are 65 inches or taller?
The probability of selecting two women 65 inches or taller is 0.25.
The probability of selecting one woman who is 65 inches or taller is 0.5 because 50% of the area of a normal curve lies to the right of its mean.
Since this is a large university, we will make the approximation that we will treat this problem as though we were selecting women WITH replacement and that the selection of the two women are random and independent selections. This allows us to multiply the probability of picking the first woman having a height greater than 65 inches by the probability of picking the second woman having a height greater than 65 inches.
Thus we can say that the probability of selecting two women whose height are at least 65 inches is (0.5)(0.5)=0.25.