1. Chapter 17 Probability Models
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Bernoulli Trials
The basis for the probability models we will examine in this chapter is the __________________.
We have Bernoulli trials if:
there are _____ possible outcomes (___________ and ____________).
the probability of success, p, is ____________.
the trials are ______________.

3. The Geometric Model
A single Bernoulli trial is usually not all that interesting.
A Geometric probability model tells us the probability for a random variable that counts the number of Bernoulli trials until the __________________.
Geometric models are completely specified by one parameter, _______________________, and are denoted Geom(__).

4. The Geometric Model (cont.)
Geometric probability model for Bernoulli trials: Geom(p)
p = probability of success
q = 1 – p = probability of failure
X = # of trials until the first success occurs
P(X = x) =

5. Independence
One of the important requirements for Bernoulli trials is that the trials be _________________.
When we don’t have an infinite population, the trials are __________________. But, there is a rule that allows us to pretend we have _________________ trials:
The ___% condition: Bernoulli trials must be independent. If that assumption is violated, it is still okay to proceed as long as the sample is smaller than ____% of the population.

6. TI Tips Under Distributions you will find both geometpdf and geometcdf
Use geometpdf(p,x) to find the probability of any ________ outcome. p is the individual probability of success and x is the number of trials until you get a success. Ex. geometpdf(.2,5) ≈
Use geometcdf(p, x) to find the probability of success ________________ the xth trial.
Ex. Geometcdf(.2, 4) ≈

7. Ex. Approximately 3.6% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists Ratkowsky and Martin (Australian Journal of Agricultural Research, Vol. 23, pp ). Bitter pit is a disease of apples resulting in a soggy core, which can be caused either by over watering the apple tree or by a calcium deficiency in the soil. Let n be a random variable that represents the first Jonathan apple chosen at random that has bitter pit.
a) Find the probability that n = 3, n = 5, n= 12.
b) Find the probability that n < 5.
c) Find the probability that n > 5.
d) State the mean and standard deviation.

8. Assignment
P. 398 #7-12

9. Chapter 17 Probability Models (2)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

10. The Binomial Model
A Binomial model tells us the probability for a random variable that counts the number of ____________ in a fixed number of __________ _________.
Two parameters define the Binomial model: ___, ___________________; and, ___, __________ _______________. We denote this Binom(n, p).

11. The Binomial Model (cont.)
In n trials, there are
ways to have k successes.
Read nCk as “______________.”
Note: n! = n x (n-1) x … x 2 x 1, and n! is read as “________________.”
(Can also be shown as)
Find the following.
a) b)
10C4

12. The Binomial Model (cont.)
Binomial probability model for Bernoulli trials: Binom(n,p)
n =
p =
q = =
X =
P(X = x) =

13. TI tips Under Distributions you will find both binompdf and binomcdf
Use binompdf(n,p,x) to find the probability of any ________ outcome. n is the number of trials, p is the individual probability of success and x is the number of successes. Ex. binompdf(5,.2,2) ≈
Use binomcdf(n,p, x) to find the probability of getting _____________________successes in n trials.
Ex. binomcdf(5,.2, 2) ≈

14. Ex. A basketball player makes 70% of his freethrows
Ex. A basketball player makes 70% of his freethrows. Assuming the shots are independent, what is the probability of each of the following?
a) He makes exactly 3 out of the next 5 attempts.
b) He makes at most 3 out of the next 5.
c) He makes at least 3 out of the next 10.

15. The Normal Model to the Rescue
As long as the ________________ Condition holds, we can use the Normal model to approximate Binomial probabilities.
Success/failure condition: A Binomial model is approximately Normal if we expect at least ___ successes and ____ failures:

16. Continuous Random Variables
When we use the Normal model to approximate the Binomial model, we are using a ___________ random variable to approximate a __________ random variable.
So, when we use the Normal model, we no longer calculate the probability that the random variable equals a ___________ value, but only that it lies _____________ two values.

17. Ex. An orchard owner knows that he’ll have to use about 6% of the apples he harvests for cider because they will have bruises or blemishes. He expects a tree to produce about 300 apples.
a) Verify that you can use the normal model to approximate the distribution.
b) Find the probability there will be no more than a dozen cider apples.
c) Is it likely there will be more than 50 cider apples? Explain.

18. What Can Go Wrong? Be sure you have Bernoulli trials.
You need ____ outcomes per trial, a constant _________________, and _______________.
Remember that the ______________ provides a reasonable substitute for _______________.
Don’t confuse ___________and _____________ models.
Don’t use the Normal approximation with ___________.
You need at least ___ successes and ____ failures to use the Normal approximation.

19. What have we learned? Geometric model Binomial model Normal model
When we’re interested in the number of Bernoulli trials __________________________.
Binomial model
When we’re interested in the number of _________ in a certain number of Bernoulli trials.
Normal model
To ______________ a Binomial model when we expect at least ___ successes and ___ failures.

20. Assignment
P. 399 #13-15, 17, 19-21, 26, 29