Download 4-3-binomial-prob

Triola – Section 4.3 – Using the TI-83 to Find Factorials, Binomial Coefficients and
Binomial Probabilities
Here is the binomial probability formula:
P( x) 
n!
 p x  q n x
(n  x)! x!
Using the notation of the binomial coefficient: n C x , the formula can be written as:
P( x) n Cx  p x  q n x or P( x)   nx   p x  q n x
where x is the number of successes in n trials, p is the probability of success in any one
trial, and q is the probability of failure in any one trial. (q = 1 – p)
1) Evaluate factorials with the calculator:
Type number
Press MATH
Arrow left to PRB
Select 4:!
Press ENTER
Examples:
a) Find 10!
10! = 10 * 9 * 8 *… * 3 * 2 * 1 =
b) Find 6!
2) Evaluate binomial coefficients with the calculator:
Type n (number of trials)
Press MATH
Arrow left to PRB
Select 3:nCr
Type x
Press ENTER
Examples:
a) Find 10 C3 =
b) Find 8 C5 =
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3) Find binomial probabilities with the calculator
A) To find individual probabilities: Use binompdf(n,p,x)
Press 2nd VARS
Select 0:binompdf(
Type n,p,x)
Press ENTER
Examples:
a) For a binomial experiment with n = 7 and p = 0.8, find P(x = 3).Use the
formula; then use the shortcut feature of the calculator to check answer.
b) For a binomial experiment with n = 4 and p = 1/3, find P(x = 2).
B) To get a list of all the probabilities corresponding to x = 0, 1, 2, …., n:
Use binompdf(n,p) and scroll to the right to read the probabilities
Examples:
a) For a binomial experiment with n = 4 and p = 1/6, find the probability
distribution.
X P(X=x)
b) For a binomial experiment with n = 5 and p = 1/2, find the probability
distribution.
X P(X=x)
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C) To calculate cumulative probabilities from 0 to x, use binomcdf(n,p,x)
Press 2nd VARS
Select A:binomcdf(
Type n,p,x)
Press ENTER
Examples:
a) For a binomial experiment with n = 7 and p = 0.2, find the probability of at
most 3 successes.
b) For a binomial experiment with n = 6 and p = 0.46, find the probability of at
most 4 successes.
c) For a binomial experiment with n = 4 and p = 0.3, find the probability of at
least 2 successes.
d) For a binomial experiment with n = 8 and p = 0.85, find the probability of at
least 5 successes.
e) For a binomial experiment with n = 9 and p = 0.35, find the P (2 < x <6)
f) For a binomial experiment with n = 10 and p = 0.73, find the probability
that x is between 4 and 9 inclusive.
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D) To graph a probability distribution follow the steps outlined below:
a) For a binomial experiment with n = 4 and p = ¼
Get into the editor of the calculator and clear two lists
Place the possible values of the random variable into one of the lists, let’s say L1
(In this case the possible values of x are from 0 to 4)
Go to L2, and arrow up until you “sit” on the name of the list
Press 2nd VARS[DISTR]
Arrow down to select 0:binompdf(
Indicate choices of n,p (It should read: binompdf(4,1/4))
Press ENTER
The probabilities should show in L2
Sketch a HISTOGRAM for L1, L2 (GO to STAT PLOT)
Select appropriate WINDOW values
x-min = 0
x-max = 5 (n + 1)
x-scale = 1
y-min = - 0.2
y-max = 0.6
Press GRAPH
The graph of the distribution should show.
Press TRACE and arrow right to see the values of the random variable
along with the probabilities.
Comment on the shape of this distribution.
b) For a binomial experiment with n = 6 and p = ½
Sketch the graph of the distribution and comment on its shape. Work on L3, L4.
Remember to have only one plot ON.
c) For a binomial experiment with n = 10 and p = 4/5
Sketch the graph of the distribution and comment on its shape. Work on L5, L6.
d) Relationship between the value of p and the shape of the binomial
distribution
If p < 0.5
the shape is
If p = 0.5
the shape is
If p > 0.5
the shape is
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