Forearm Length. In 1903, K. Pearson and A. Lee published a paper entitled “On the Laws of Inheritance in Man. I. Inheritance of Physical Characters” (Biometrika, Vol. 2, pp. 357–462). From information presented in that paper, forearm length of men, measured from the elbow to the middle fingertip, is (roughly) normally distributed with a mean of 18.8 inches and a standard deviation of 1.1 inches. Let x denote forearm length, in inches, for men.
a. Sketch the distribution of the variable x.
b. Obtain the standardized version, z, of x.
c. Identify and sketch the distribution of z.
d. The area under the normal curve with parameters 18.8 and 1.1 that lies between 17 and 20 is 0.8115. Determine the probability that a randomly selected man will have a forearm length between 17 inches and 20 inches.
e. The percentage of men who have forearm length less than 16 inches equals the area under the standard normal curve that lies to the of______.