Using graph(s), shading, and appropriate probability distribution table, and assuming that the heights of women are normally distributed, with a mean of 65.0 inches and a standard deviation of 2.5 inches, and assuming that men have heights that 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. Determine what percentage of people of your gender would be taller than you are. In case your height is "exactly" 65 inches, add 1 inch to it and work with 66 inches.
(b) If someone of your gender is randomly selected what is the probability that the selected person would be shorter than you are?
(c) What is the minimum height of a person of your gender to join the "Top 15% Tall Club"?
(d) If 144 people of your gender are randomly selected, determine the probability that their mean height would exceed your height.
(de) If 25 people of mixed gender, with a mean height of 67 inches and standard deviation of 2.60 inches are randomly selected from a normally distributed population, construct a 95% confidence interval for the mean of the population