Page 185 - Probability Demystified

174 CHAPTER 9 The Normal Distribution

13. The area under the standard normal distribution between z ¼ 1.7
and z ¼ 0.5 is
a. 69.2%
b. 4.5%
c. 35.6%
d. 64.7%

14. An exam which is approximately normally distributed has a mean of
200 and a standard deviation of 20. If a person who took the exam is
selected at random, find the probability that the person scored above
230.

a. 93.3%
b. 70.2%
c. 6.7%
d. 30.8%
15. The average height for adult females is 64 inches. Assume the variable
is normally distributed with a standard deviation of 2 inches. If a
female is randomly selected, find the probability that her height is
between 62 and 66.8 inches.
a. 92%
b. 76%
c. 32%
d. 16%

Probability Sidelight

A BRIEF HISTORY OF THE NORMAL DISTRIBUTION

The applications of the normal distribution are many and varied. It is used
in astronomy, biology, business, education, medicine, engineering, psychol-
ogy, and many other areas. The development of the concepts of the normal
distribution is quite interesting.
It is believed that the first mathematician to discover some of the concepts
associated with the normal distribution was the English mathematician,
Abraham de Moivre (1667–1754). He was born in France, but moved to
England because of the French government’s restrictions on religion and civil
liberties. He supported himself by becoming a private tutor in mathematics.