Download Lesson 18 Nov IV

Math Tech IIII, Nov 18
The Binomial Distribution III
Book Sections: 4.2
Essential Questions: How can I compute the probability of any event?
How can I create a discrete binomial probability distribution and
how do I compute binomial statistics?
Standards: DA-5.6, S.MD.1, .2, .3
The Universal First Step
• Identify n, p, and x (if it applies) or all possible values
of x in your problem.
 p may be given or it may not. If not, enough information will
be given to figure it out. Either way, you must have p.
• Important point – no one is ever going to give you q. If
you need it, YOU are going to have to find it. How?
 q=1-p
Remember
• In a discrete probability distribution, which a binomial
distribution is, the expected value and the mean are the
same thing.
Binomial Probability Distributions
• Creating a discrete binomial probability distribution:
To construct a binomial distribution table, open STAT
Editor
1) type in 0 to n in L1
2) Move cursor to top of L2 column (so L2 is hi lighted)
3) Type in command binomialpdf(n, p, L1) and L2 gets
the probabilities.
Example
Produce a binomial probability distribution for n = 8, p = 0.54, and
x = 0 – 8.
Put 0 – 8 into L1
Place cursor on name of L1
Type in binomialpdf(8, .54, L1)
The result
Example 1
• Produce a discrete binomial probability distribution for the
following: n = 4, p = 0.53.
• Use as much of the template as required to build your distribution.
X
P(x)
Example 1a
• Three in five beagle puppies have their eyes open within 7 days of
their birth. James’ beagle had a litter of 6 pups 7 days ago.
Produce a discrete probability distribution for this binomial
experiment.
X
P(x)
0
1
2
3
4
5
6
Binomial Statistics
• Because of the nature of this distribution, binomial
mean, variance, and standard deviation are almost
trivial. Here are the formulas:
Mean
μ = np
σ2 = npq Variance
σ = npq
Standard deviation
One other pearl of wisdom – You could always compute
mu (μ) and sigma (σ) using the 1-var stat L1, L2
computation on the calculator {providing you have the
distribution in L1 and L2}
How Do You Do It?
• To compute binomial statistics:
1. Find n, p, and q
2. Plug and chug into the formulas:
μ = np
σ2 = npq
σ = npq
Mean
Variance
Standard deviation
Modified Formulas for Less Fun
Mean, there is no changing this one
μ = np
Variance, forget about it.
σ2 = npq
σ = (n  p  (1  p))  .5 Standard deviation, put it on the calculator
just like this. Now you only need n and p.
Example 2
• An archer has an 80% chance of hitting a target at 50 yards. The
archer shoots 5 arrows. What are the mean and standard deviation of
the probability distribution for this situation?
Example 3
• In Phoenix, Arizona, about 92% of the days in a year are
sunny. Find the mean and standard deviation of the
number of sunny days during the month of February.
Example 4
• The 2010 census has concluded that 16% of American
households own 2 or more pets. What is the mean and
standard deviation of the number of American
households out of 12 that would have two pets?
Example 1a, The Other Way
• Three in five beagle puppies have their eyes open within 7 days of
their birth. James’ beagle had a litter of 6 pups 7 days ago.
Produce a discrete probability distribution for this binomial
experiment.
X
P(x)
0
1
2
3
4
5
6
Final Thought
• Probability is, was, and will be a number
between 0 and 1, it can be 0 and it can be 1.
Computing Probability
• There are 5 computations you need to know how to
accomplish in binomial probability which are:
x = #, x < #, x > #, x ≤ # and x ≥ #
• Use the computation sheet in any probability to set the
problem up
• How will you know that you are computing a
probability? Answer – The problem will say it.
Classwork: CW 11/18/16, 1-12
Homework – None