Figure 1: Normal Distribution a. What is your height? Which percentage of the height distribution do you happen to be in? Hint: The mean height for women in the US is 5 ft 4 in and the standard deviation of the height distribution for women is 2.5 inches The mean height for men in the US is 5 f Sin and the standard deviation of the height distribution for men is 3 inches.b. Peter Dinklage won several awards for that great performance. In his own words, Dinklage's character was "..guilty of being a dwarf. "And he was on trial for that reason alone. Remembering that Dinklage is 4 A 4 inches, which percentage of the height distribution does he happen to be fall into?c. Your instructor's favorite NBA player is Jimmy Butler, aka Jimmy Buckets. Butler is the shooting guard for Miami Heat and 6ft Tin tall. Which percentage of the height distribution does Butler fall into?d. Your instructor is 5 A 3 inches tall. What percentage of the height distribution does your instructor fall into?E. The height distribution does not remain constant over time. The mean height for both women and men increases over decades. If we go back thousands of years in time, we can see that individuals used to be significantly shorter.As an example, archeological remains from the Mesolithic (10,000 years ago) indicate that women's average height was around 5 ft 1 inch and men's average height was around 5 A 5 inches at the time. Suppose you find a time machine and travel back in time 10 thousand years. What percentage of the height distribution would you fall into? (Hint: You can assume a standard deviation of 2.5 inches for women and 3 inches for men.)f. The height distribution is not the same across countries either. As an example, in Indonesia the average height of men is 5 A 2 inches, and the average height of women is 4 A 10 inches.G. Suppose you travel to Jakarta, capital of Indonesia. What percentage of the height distribution would you fall into? (Hint: You can assume a standard deviation of 2.5 inches for women and 3 inches for men.)