Transcript 6.3 Geometric Distribution reformatted

Warm-up
6.3 Geometric Distribution and 6.1 and 6.2 Quiz
Suppose you flip a fair coin 8 times.
1) What is the probability that you get heads 3 times?
2) At least 25% heads?
3) Exactly 25% heads?
4) What will be the expected value?
5) What is the standard deviation?
6.2 E #23 - 25
Binompdf (5, 6/36, 1)
Binompdf(5, 6/36, 3)
1- Binompdf (5, 6/36,0)
Binomcdf (5, 6/36, 1)
Binompdf(5,0.5,3)
6.2 H.W. Answers continued…
Binompdf(5, 54/90,1)
1- Binompdf(5,54/90,0)
1 – Binomcdf (25, 0.127, 1)
Information about A.P. Exam Registration
Hi team,
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Thank you,
Kathy Presby M.A.
Student of the day!
Block 4
Student of the day!
Block 5
6.3 Geometric Distribution
• Same as Binomial Distribution
Success or Failure, p doesn’t change over trials and each
trial is independent of each other
• Only difference is x or k represents how many trials occur
until there is the first success.
• The # of trials that occur is often called the waiting time
• There is no fixed number of trials, only the # of trials until
the first success occurs. P ( X  k )  (1  p ) k 1 p
Example : About 10% of the U.S. population has type B
blood. What is the probability that the third donation a
blood bank technician checks is type B?
k = # of trials
P ( X  k )  (1  p )
k 1
P ( X  1)  (1  0 . 1)
1 1
P ( X  2 )  (1  0 . 1)
p
On the 1st try, what is the
probability that the event occurs?
0 .1
2 1
0 .1
Delores has a free-shooting percentage of 0.65.
What is the probability that the first free throw she manages to
make is on her 4th attempt.
Characteristics of Geometric Distributions
and how to use the formulas
Problem: The probability of a type A blood donation is 0.4. On average,
how many donations will the blood bank technician have to
check before they find a donation of type A blood.
Number of trials for 2 Successes
Let’s say the blood bank technician needs to find two
donations of type A blood.
Practice Problem
The phone line for a 24-hour ticket office is busy about
70% of the time.
a. If you dial at random times throughout the week, what
is the expected number of tries it will take you to get
through? What is the standard deviation of the number
of tries?
b. What is the expected total number of times you will
have to dial if you forget to ask a question after getting
through the first time and have to call again.
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Directions for Quiz and H.W.
Work on the quiz carefully.
When you finish turn it in at the front of the class.
Read 6.3, define the terms and copy the definitions.
Next block bring your chosen assignment: A.P Practice of Ch.
5 and 6 OR One-Boy Family Planning
• Also have your notes ready for the Notebook Check
Terms: Expected Value (6.1), Linear Transformation (6.1),
Binomial Dist. (6.2), Geometric Dist.(6.3)
Formulas: Expected Value(6.1), Variance(6.1), Linear
Transformation (6.1), Addition and Subtraction Rules for
Random Variables (6.1), Probability formula for Binomial
Distribution (6.2), Binomial Distr. Mean and S. D. formula(6.2) ,
Geometric Dist. Formula (6.3), Mean and S.D. of Geometric
Dist. (6.3) : 14 in all ( 14 x 2 = 28 pts) 6. 1 to 6.3 5 + warm-ups
(5 x 14 pts = 70 pts) 10 notes 4 warm-up 28 + 70 = 98
Next couple of classes
February 6th (Monday) A.P. Statistics finish notes
on 6.3 and start on selected assignment
1st day of Ntbk Check
February 8th (Wednesday) Practice Ch. 6 Test and
finish selected assignment.
Ch. 6 Test on Friday February 9th!