Page 132 - Probability Demystified

CHAPTER 7 The Binomial Distribution 121

1
4. n ¼ 8, x ¼ 3, p ¼
2
5
3
1 1
Pð3 headsÞ¼ C 3
8
2 2

1 1
¼ 56
8 32
1
¼ 56
256
7
¼ ¼ 0:21875
32
2
5. n ¼ 4, x ¼ 3, p ¼
3
2 3 1 1
Pð3 red marblesÞ¼ C 3
4
3 3
8
¼ 4
81
32
¼ 0:395
81

The Mean and Standard Deviation for a

Binomial Distribution

Suppose you roll a die many times and record the number of threes you
obtain. Is it possible to predict ahead of time the average number of threes
you will obtain? The answer is ‘‘Yes.’’ It is called expected value or the mean
of a binomial distribution. This mean can be found by using the formula
mean ( ) ¼ np where n is the number of times the experiment is repeated and
p is the probability of a success. The symbol for the mean is the Greek letter
(mu).

EXAMPLE: A die is tossed 180 times and the number of threes obtained is
recorded. Find the mean or expected number of threes.