Download 4) Find binomial probabilities with a shortcut feature

Math 116 – Activity 6 (Section 5.2)
Objective: Using the TI-83/84 calculator to find Factorials, Binomial Coefficients and
Binomial Probabilities
Section 5.2 - Here is the binomial probability formula
P(r ) 
n!
 p r  q nr = Cn,r  p r  q nr
(n  r )!r !
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)
Section 5.3 - Mean, Variance, and Standard Deviation for the Binomial Distribution
In Section 5.1, we used the general formulas for any discrete probability distribution. But the
special qualities of binomials distributions, lead to specialized formulas for binomials
Both sets of formulas are here
Any Discrete Probability
Distribution
Section 5.1
Mean
Standard Deviation
  [ x  P( x)]

[ x
2
 P( x)]   2
Binomial Distributions
Section 5.3
  np
  npq
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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 =
3) Evaluate binomial probabilities with the formula:
For a binomial experiment with n = 7 and p = 0.8,
a) Find P(r = 3)
b) Find P(r = 6)
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4) Find binomial probabilities with a shortcut feature of 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(r = 3).
b) For a binomial experiment with n = 4 and p = 1/3, find P(r = 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. Find the mean and standard deviation for the distribution. Identify
usual and unusual values with the range rule of thumb and with the probability
rule.
X P(X=r)
b) For a binomial experiment with n = 5 and p = 1/2, find the probability
distribution. Find the mean and standard deviation for the distribution. Identify
usual and unusual values with the range rule of thumb and with the probability
rule.
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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