354 PART 7 The Part of Tens

The Binomial Distribution

The binomial distribution helps you estimate the probability of getting x successes

out of N independent tries when the probability of success on one try is p. (See

Chapter 3 for an introduction to probability.) A common example of the binomial

distribution is the probability of getting x heads out of N flips of a coin. If the coin

is fair, p = 0.5, but if it is lopsided, p could be greater than or less than 0.5 (such

as p = 0.7). Figure 24-4 shows the frequency distributions of three binomial dis-

tributions, all having p

0 7. but having different N values.

The formula for the probability of getting x successes in N tries when the proba-

bility of success on one try is p is Pr

,

,

1

! /

!

!

(

x N p

p

N

x N

x

N

x

)

)

[

p ^x

.

Looking across Figure 24-4, you might have guessed that as N gets larger, the

binomial distribution’s shape approaches that of a normal distribution with mean

Np and standard deviation

Np

p

(

)

1

.

FIGURE 24-3:

The log-normal

distribution.

© John Wiley & Sons, Inc.

FIGURE 24-4:

The binomial

distribution.

© John Wiley & Sons, Inc.