Page 135 - Probability Demystified

124 CHAPTER 7 The Binomial Distribution

mean: ¼ np
¼ 100ð0:80Þ
¼ 80

p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
standard deviation: npð1 pÞ
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
¼ 100ð0:8Þð0:2Þ
p ffiffiffiffiffi
¼ 16
¼ 4
Approximate range of values:

2 < most values < þ 2 ð Þ
80 2 ð4Þ < most values < 80 þ 2 ð4Þ
72 < most values < 88
Hence, most of his scores will be somewhere between 72 and 88.

Note: The concept of the standard deviation is much more complex than
what is presented here. Additional information on the standard deviation will
be presented in Chapter 9. More information on the standard deviation can
also be found in all statistics textbooks.

PRACTICE

1. Twenty cards are selected from a deck of 52 cards. Each card is
replaced before the next card is selected. Find the mean and standard
deviation of the number of clubs selected.
2. A coin is tossed 1000 times. Find the mean and standard deviation of
the number of heads that will occur.
3. A 50-question multiple choice exam is given. There are four choices
for each question. Find the mean and standard deviation of the
number of correct answers a student will get if he selects each answer
at random.
4. A die is rolled 720 times. Find the mean, standard deviation, and
approximate range of values for the number of threes obtained.
5. A factory manufactures microchips of which 4% are defective. Find
the average number of defective microchips in a lot of 500. Also, find
the standard deviation and approximate range of values.