Bluman, Chapter 5 1 - navimath...Bluman, Chapter 5 17 3 0.30 0.70 5! 32 2!3! P n p X o 5, 0.30,"at...
Transcript of Bluman, Chapter 5 1 - navimath...Bluman, Chapter 5 17 3 0.30 0.70 5! 32 2!3! P n p X o 5, 0.30,"at...
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Bluman, Chapter 5 1
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guessing
Suppose there is multiple choice quiz on
a subject you don’t know anything
about…. 15th Century Russian Literature;
Nuclear physics etc.
You have to guess on every question.
There are 5 questions and each question
has 4 choices.
Bluman, Chapter 5 2
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Let x be the score on the test.
Find p(x=0)
In another words the probability you will get
a score of zero, i.e. you will get all the
questions wrong
Find p(x=1)
In another words the probability you will get
a score of 1, i.e. you will get only one
question correct.
Bluman, Chapter 5 3
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Bluman, Chapter 5 4
Question
number
Correct or wrong
1
2
3
4
5
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Repeat the process:
P(2)=
P(3)=
p(4)=
P(5)=
Bluman, Chapter 5 5
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What if the number of questions
changed
Let’s say now the test has 10 questions
and each question has 4 choices.
What does the probability distribution chart
looks like?
Bluman, Chapter 5 6
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Bluman, Chapter 5 7
x P(x)
0
1
2
3
4
5
6
7
8
9
10
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What if the number of choices
changes
Let’s say now the test has 10 questions
and each question has 5 choices.
What does the probability distribution chart
looks like?
Bluman, Chapter 5 8
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Bluman, Chapter 5 9
1
2
3
4
5
6
7
8
9
10
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5-3 The Binomial Distribution
10
Many types of probability problems have
only two possible outcomes or they can be
reduced to two outcomes.
Examples include:
when a coin is tossed it can land on heads or
tails,
when a baby is born it is either a boy or girl.
It will rain or it won’t
A person will pass the bar exam or not.
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The Binomial Distribution
Bluman, Chapter 5 11
The binomial experiment is a probability
experiment that satisfies these requirements:
1. Each trial can have only two possible
outcomes—success or failure.
2. There must be a fixed number of trials.
3. The outcomes of each trial must be
independent of each other.
4. The probability of success must remain the
same for each trial.
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Notation for the Binomial Distribution
Bluman, Chapter 5 12
The symbol for the probability of success
The symbol for the probability of failure
The numerical probability of success
The numerical probability of failure
and P(F) = 1 – p = q
The number of trials
The number of successes
P(S)
P(F)
p
q
P(S) = p
n
X
Note that X = 0, 1, 2, 3,...,n
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The Binomial Distribution
!
- ! !
X n XnP X p q
n X X
Bluman, Chapter 5 13
In a binomial experiment, the probability of
exactly X successes in n trials is
number of possible probability of adesired outcomes desired outcome
or
X n X
n xP X C p q
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Chapter 5
Discrete Probability Distributions
Section 5-3
Example 5-16
Page #272
Bluman, Chapter 5 14
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Example 5-16: Survey on Doctor Visits
A survey found that one out of five Americans say
he or she has visited a doctor in any given month.
If 10 people are selected at random, find the
probability that exactly 3 will have visited a doctor
last month.
Bluman, Chapter 5 15
!
- ! !
X n XnP X p q
n X X
3 7
10! 1 43
7!3! 5 5
P
15
10,"one out of five" , 3 n p X
0.201
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Chapter 5
Discrete Probability Distributions
Section 5-3
Example 5-17
Page #273
Bluman, Chapter 5 16
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Example 5-17: Survey on Employment A survey from Teenage Research Unlimited
(Northbrook, Illinois) found that 30% of teenage
consumers receive their spending money from
part-time jobs. If 5 teenagers are selected at
random, find the probability that at least 3 of them
will have part-time jobs.
Bluman, Chapter 5 17
3 25!
3 0.30 0.702!3!
P
5, 0.30,"at least 3" 3,4,5 n p X
0.132
4 15!
4 0.30 0.701!4!
P 0.028
5 05!
5 0.30 0.700!5!
P 0.002
3 0.132
0.028
0.002
0.162
P X
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Chapter 5
Discrete Probability Distributions
Section 5-3
Example 5-18
Page #273
Bluman, Chapter 5 18
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Example 5-18: Tossing Coins
A coin is tossed 3 times. Find the probability of
getting exactly two heads, using Table B.
Bluman, Chapter 5 19
12
3, 0.5, 2 n p X 2 0.375 P
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The Binomial Distribution
Mean: np
2Variance: npq
Bluman, Chapter 5 20
The mean, variance, and standard deviation
of a variable that has the binomial distribution
can be found by using the following formulas.
Standard Deviation: npq
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Chapter 5
Discrete Probability Distributions
Section 5-3
Example 5-23
Page #276
Bluman, Chapter 5 21
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Example 5-23: Likelihood of Twins The Statistical Bulletin published by Metropolitan
Life Insurance Co. reported that 2% of all American
births result in twins. If a random sample of 8000
births is taken, find the mean, variance, and
standard deviation of the number of births that
would result in twins.
Bluman, Chapter 5 22
8000 0.02 160 np
2 8000 0.02 0.98 156.8 157 npq
8000 0.02 0.98 12.5 13 npq
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Tech notes
Read technology
notes on page
281.
Read example 5-
19 on page 274
Exercises 5.3
Page 276 #1,
5, 11, 15 and
17
Bluman, Chapter 5 23