Problem VH [20 points] For this problem, you should show, or briey explain, your work involving graph(s), shading, and appropriate probability distribution table(s)r'formula(s)fapplet(s). Show probability values to preferably four decimal places, If the heights of women are normally distributed with a mean of 65.0 inches and a standard deviation of 2.5 inches and the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches, (a) Calculate and write down your height in inches. (b) Determine the probability of nding a person of your gender to be exactly at your height. (c) Determine what percentage of people of your gender would be taller than you are. In case your height is \"exactly\" 65 inches or 69 inches, add 1 inch to it and keep working with that new height for this and the remaining parts of the problem. ((1) If someone of your gender were randomly selected, what would be the probability that the selected person would be shorter than you are? (e) What is the probability for the height of a person of your gender to be within 2 inches of your height (between \"your height 2 inches\" and \"your height + 2 inches" ? (D What is the minimum height of a person of your gender to be eligible for joining the \"Top 16% Tall Club\"? (g) If 81 people of your gender are randomly selected, determine the probability that your height would exceed their mean height