Stats 4 Day 11
Homework and
Agenda
•
Homework Due Monday 2/1
• Chapter 16, page 369
• #1-7, #16-18
Agenda:
• 1. Do Now and go over practice
• 2. A little more practice
• 3. Standard Deviation with Expected Value
• 4. Practice sheet
Tomorrow: SD and GAME
The Greedy Pig
•
Do Now
•
Your company bids for two contracts. You believe
the probability you get contract 1 is 0.8. If you
get contract 1, the probability you also get
contract 2 will be .2, and if you do not get
contract 1, the probability you still get contract 2
is 0.3. Let X be the number of contracts you get.
Create a probability model and find the expected
value (E(x)=μ) for the number of contracts.
Review Practice
Worksheet from
Yesterday
•
Presentation Volunteers for Extra
Credit
A little more practice
•
In pairs, complete the half sheet
Standard Deviation
•
What did standard deviation measure
again?
SPREAD!
What does standard deviation mean
again?
• (How far each data point is from the
______________)
AVERAGE!
•
•
What if I told you that the expected
value (the average of your possible
outcomes given their probabilities) for
one of our card games is $1.21, but the
standard deviation of that expected
value is $100, would you still want to
play? The Standard Deviation of the
Expected Value contributes to the
meaning of the Expected Value as a
statistic. It tells us more about the
data!
•
•
Finding the Standard
Deviation of a Random
Variable
How far does each value deviate from the average
(the expected value)??
Outcome
Value
X
Probability
P(X)
Deviation Squared
(X-E(X))2 or (X-μ)2
Standard Deviation: the average (the expected
value) of the deviations!
•
But, we have to make sure the deviations are positive, so
we square them
•
Multiply and add (like before)
•
Then undo the square (square root)!
Steps to Find SD of
the Random Variable
1.
2.
3.
4.
5.
6.
Make Probability Model
Calculate E(X) (aka μ), the expected
value
Add Deviations column to table and
Calculate the deviations, X-E(X)
Square the deviations and multiply
by their probabilities
Add
Square Root
Practice 1: our Do
Now
•
•
Your company bids for two contracts. You believe
the probability you get contract 1 is 0.8. If you
get contract 1, the probability you also get
contract 2 will be .2, and if you do not get
contract 1, the probability you still get contract 2
is 0.3. Let X be the number of contracts you get.
Create a probability model and find the expected
value (E(x)=μ) for the number of contracts.
Find the Standard Deviation!
Practice 1
•
I invested $30,000 in a company this
year. There is a 1% chance they fail
and I lose my money, there is a 55%
chance that I make a 10% return
(that I make $3,000), the remaining
percent of the time I will likely make
a 30% return (that is, I will make
$9,000). What is my expected value
for my return and what is the
standard deviation?
Practice half sheet