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Part III: Distributions and the Central Limit Theorem
The final probability distribution for X is shown in Table 8-2. Notice these
probabilities all sum to 1 because every possible value of X is listed and
accounted for.
Probability Distribution for X = Number
Table 8-2
of Red Traffic Lights (n = 3, p = 0.30)

X
0
0.343
1
0.441
0.189
2
3
0.027
Finding Probabilities Using p(x)
the Binomial Table
The previous section deals with values of n that are pretty small, but you may
wonder how you are going to handle the formula for calculating binomial prob-
abilities when n gets large. No worries! A large range of binomial probabilities
are provided in the binomial table in the appendix. Here’s how to use it:
Within the binomial table you see several mini-tables; each one corresponds
with a different n for a binomial (n = 1, 2, 3, ..., 15, and 20 are available). Each
mini-table has rows and columns. Running down the side of any mini-table, you
see all the possible values of X from 0 through n, each with its own row. The col-
umns of the binomial table represent various values of p from 0.10 through 0.90.
Finding probabilities for
specific values of X
To use the binomial table in the appendix to find probabilities for X = total
number of successes in n trials where p is the probability of success on any
individual trial, follow these steps:

1. Find the mini-table associated with your particular value of n (the
number of trials).

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