Download Sample 5.3.B.2 Complete

4C.S.MD.1.2.3.4.12.8.11
2011
Domain: Probability & Statistics
Cluster: Calculated expected values and use them to solve problems.
Standards: 1. (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample
space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
2. (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
3. (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be
calculated;find the expected value. For example, find the theoretical probability distribution for the number of correct answers
obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected
grade under various grading schemes.
4. (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned
empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the
United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100
randomly selected households?
Essential Questions
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Why are probability
distributions used?
How can
probability
distributions be
used with real-life
problems?
In what other
disciplines besides
statistics is expected
value used in?
Provide examples.
Content Statements
Enduring Understandings
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Defining random
variables allows us to
navigate through
probability distributions.
Probability distributions
gives us tools to describe
variables of interest in
our world.
Expected values can be
used in a variety of
contexts outside of
probability and statistics,
such as biology.
Activities, Investigation, and Student Experiences
Examples/activities that can be done with the students are:
1. TI Inspire Activity:
http://education.ti.com/xchange/US/Math/Statistics/8
971/RollTheDice_Student.pdf
2. Find the means of the given probability distributions.
a. The probabilities that a batch of 4 computers will
contain 0, 1, 2, 3, and 4 defective computers are
0.5470, 0.3562, 0.0870, 0.0094, and 0.0004,
respectively. Round answer to the nearest hundredth.
b. A police department reports that the probabilities that
0, 1, 2, and 3 burglaries will be reported in a given
day are 0.50, 0.38, 0.11, and 0.01, respectively.
4C.S.MD.1.2.3.4.12.8.11
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Students will
understand that
typically the graph
of a probability
distribution is a
histogram.
Students will be
able to
differentiate
between a discrete
and continuous
random variable.
Students will
understand
expected values
are used to
calculate an
expected payoff.
Students will
understand to
calculate an
expected value you
take sum of the
products of each
random variable
value and its
corresponding
probability value.
Assessments
2011
3. Calculate the expected gross winnings for the $1 BIG
BEAR ticket with probabilities given below.
Prize Probability
$1 prize with probability 1/10
$2 prize with probability 1/10.64
$3 prize with probability 1/20
$10 prize with probability 1/166.67
$20 prize with probability 1/500
$30 prize with probability 1/750
$500 prize with probability 1/60,000
$5,000 prize with probability 1/240,000
Source: http://sakowskimath.com/Principles/11_8.htm
4C.S.MD.1.2.3.4.12.8.11
2011
1. When you give a casino $5 for a bet on the number 7 in
roulette, you have a 1/38 probability of winning $175
and a 37/38 probability of losing $5. If you bet $5 that
the outcome is an odd number, the probability of winning
$5 is 18/38 and the probability of losing $5 is 20/38.
a. If you bet $5 on number 7, what is your expected
value?
b. If you bet $5 that the outcome is an odd number,
what is your expected value?
c. Which of these options is best: bet on 7, bet on
odd, or don’t bet? Why?
2. The CNA Insurance Company charges a person $250 for
a one-year $100,000 life insurance policy. Because the
person is a 21 year old male, there is a 0.9985 probability
that he will live for a year.
a. From the person’s perspective, what are the
values of the two different outcomes?
b. If the person purchases the policy, what is his
expected value?
3. Create a problem that uses probability and create a
probability distribution for your random variable.
Your problem must use real data that can be found on
the internet, newspapers, magazines, etc. Be sure to
cite the resource you used.
Equipment Needed:
Teacher Resources:
Calculators
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Whiteboards
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Overhead Projectors
Smart board
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Computers - Microsoft Excel
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http://www.khanacademy.org/video/expected-value-e-x?playlist=Probability
http://www.khanacademy.org/video/expected-valueof-binomial-distribution?playlist=Probability
http://www.khanacademy.org/video/introduction-torandom-variables?playlist=Probability
http://stattrek.com/lesson2/discretecontinuous.aspx
4C.S.MD.1.2.3.4.12.8.11
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2011
http://mathforum.org/library/drmath/view/56578.ht
ml
http://www.onlinemathlearning.com/expectedvalue.html
http://www.statisticshowto.com/articles/how-tofigure-out-an-expected-value-in-statistics/
http://in.answers.yahoo.com/question/index?qid=200
80406212018AAFRkn1