Transcript 5 Minute Check, 26 Sep

Math Tech IIII, May 4
The Binomial Distribution IV
Book Sections: 4.2
Essential Questions: How can I compute the probability of any event?
What do I need to know about the binomial distribution to pass the
Unit 7 Test?
Standards: DA-5.6, S.MD.1, .2, .3
The List of Knows
• Know the following:
 Know the four binomial conditions/characteristics
 Recognize a binomial distribution, or when it applies in a
probability problem
 Be able to compute binomial probability
 Know what is meant by a cumulative binomial distribution
and when it applies
 Be able to create and use a binomial probability distribution
 Know how to compute the mean (μ) and standard deviation
(σ) of a binomial distribution
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
Any Binomial Computation
• The probability of any equality/inequality of x successes in
n trials.
• Exactly x (x = ) binomialpdf(n, p, x)
• At most x (x ≤ ) binomialcdf(n, p, x)
Use these adjustments for any other inequality binomial
computation
• Fewer than x (x <) binomialcdf(n, p, x -1)
• At least x (x ≥) 1 – binomialcdf(n, p, x- 1)
• More than x (x >) 1 – binomialcdf(n, p, x)
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
Example 1
• The mailing list of an agency that markets scuba-diving trips to
Hawaii contains 65% males and 35% females. The agency calls
6 people chosen at random from their list. What is the
probability that they call
A) Fewer than 3 females
B) More than 2 males
Example 1a
• The mailing list of an agency that markets scuba-diving trips to
Hawaii contains 65% males and 35% females. The agency calls
10 people chosen at random from their list.
• If 10 people were called, what is the mean number of females
who would be called:
• What is the standard deviation?
What Makes a Binomial Experiment?
• A binomial experiment is a probability experiment that
satisfies the following conditions:
1.
2.
3.
4.
Contains a fixed number of trials that are all independent.
All outcomes are categorized as successes or failures.
The probability of a success (p) is the same for each trial.
There is a computation for the probability of a specific
number of successes.
Binomial Notation
• Binomial computations are known as probability by
formula. The formula has a set of arguments that you
must know and understand in application. Here is that
notation:
Symbol
n
p
q
x
Description
The number of times a trial is repeated
The probability of success in a single trial
The probability of failure in a single trial (q = 1 – p)
The random variable represents a count of the number
of successes in n trials: x = 0, 1, 2, 3, …, n
Binomial Computation III
• Creating a binomial distribution and graph:
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 hilighted)
3) Type in command binomialpdf(n, p, L1) and L2 gets
the probabilities.
4) Go to stat plot and set up appropriate graph.
Example 2
• Three in five beagle puppies have their eyes open within 7 days of
their birth. James’ beagle had a litter of 5 pups 7 days ago. Produce
a discrete probability distribution for this binomial situation.
• What is the probability that 2 or 3 pups have their eyes open in 7
days?
Final Thought
• Probability is always a number between 0 and 1,
it can be 0 and it can be 1.
Classwork: CW 5/4/15, 1-11 (PreTest)
Homework – None