American women’s heights are approximately normally distributed with mean 63.8 inches and standard deviation 4.2 inches. American men’s heights are approximately normally distributed with mean 69.4 inches and standard deviation 4.7 inches.
a. Tamara De Treaux played the role of the alien in the movie ‘E.T., the Extra-Terrestrial.’ She was 31 inches tall. Find the z-score of 31 inches for the women’s height distribution. What does it mean in this situation?
b. Verne Troyer played the role of Mini-Me in the ‘Austin Powers’ movie series. He is 32 inches tall. Find the z-score of 32 inches for the men’s height distribution. What does it mean in this situation?
c. Who has the relative smaller height, De Treaux or Troyer?
d. Does De Treaux have an unusual height for women? How about Troyer for men? Explain.