Binomial Distribution or Binomial PDF
In order to get a binomial distribution, we must
start out with a
Binomial Experiment:
1. The same activity is repeated a fixed
number of times
Examples:
Each repetition is called a
n=
2. Each trial has only 2 possible outcomes:
____________ or ______________
p=
q=
p + q = _____
3. The trials must be independent
4. In each trial, p and q remain the same
Ex. Suppose I roll a single die 5 times. I am
interested in how many times I roll a “6”.
Trial:
n=
success =
p=
failure =
q=
Are the trials independent? Why?
The outcomes of a binomial experiment fit a
Binomial Distribution.
We write:
X~B(n,p)
n and p are called
μ = mean = expected value =
σ = standard deviation =
Ex. According to a recent article, 60% of U.S. adults
say they experienced a sleep problem in the last year.
8 U.S. adults are randomly surveyed. We are
interested in the number who say that they
experienced a sleep problem in the last year.
a. Define the random variable in words.
X=
b. X ~
c. How may people out of 8 do we expect to have
experienced a sleep problem?
What is the
standard deviation?
d. Calculate the PDF.
x
0
1
2
3
4
5
6
7
8
P(x)
e. What is the probability that exactly 4 will have
experienced a sleep problem?
f. What is the probability that at most 6 will have
experienced a sleep problem?
g. What is the probability that more than 6 will have
experienced a sleep problem?
h. What is the probability that at least 6 will have
experienced a sleep problem?
Chapter 4 Calculator Instructions TI83/84
To access the discrete Distributions:
From the Home Screen:
1. Press 2nd DISTR (above the VARS key, next to CLEAR)
2. Arrow down to the desired distributions:
 0: binomialpdf(
 A: binomialcdf(
 B: poissonpdf(
 C: poissoncdf(
3. Press ENTER
4. Once you have found the correct function, enter the
parameters after the open parenthesis as given below.
Then press ENTER.
To calculate the
probability:
P(X = x)
P(X  x)
P(X< x)
P(X>x)
P(X  x)
Enter on your calculator
TI83 Binomial
TI83 Poisson
binomialpdf(n, p, x)
poissonpdf(μ, x)
binomialcdf(n, p, x)
poissoncdf(μ, x)
binomialcdf(n, p, x-1)
poissoncdf(μ, x-1)
1 – binomialcdf(n, p, x)
1 – poissoncdf(μ, x)
1 – binomialcdf(n, p, x-1) 1 – poissoncdf(μ, x-1)
Translating Expressions
X is at least 4
X is more than 4
X is at most 4
X is less than 4
X 4
X 4
X 4
X 4