Question

both distributions are approximately normal. suppose we randomly select a man and a woman from each population, and calculate the difference between their heights. we can assume that their heights are independent. find the probability that the woman is taller than the man.

Answer 1

To find the probability that the woman is taller than the man, we need to compare the heights of the two populations using the properties of the normal distribution.

Step-by-step explanation:

To find the probability that the woman is taller than the man, we need to compare the heights of the two populations. Since both distributions are approximately normal, we can use the properties of the normal distribution to solve this problem.

Let's define X1 as the height of the man and X2 as the height of the woman. The difference between their heights is given by X = X2 - X1.

To calculate the probability that the woman is taller, we need to find the area under the normal distribution curve where X > 0. We can use the properties of the standard normal distribution and the known standard deviations of the populations to calculate this probability.