Download Section 6.3 Second Day Binomial Probabilities on the TI, Mean and

Section 6.3
Second Day
Binomial Calculations on the TI
µ and σ of a Binomial RV
Is this a binomial setting?
Deal 10 cards from a well-shuffled deck of
cards. Let X = the number of red cards. Is
this a binomial distribution?


If so, what are n and p?
If not, why not?
Using the Calculator to Find
Binomial Probabilities
Under 2nd DISTR, find 0:binompdf(
This command finds probabilities for the
binomial probability distribution function.
The parameters for this command are
n, p, k IN THAT ORDER.
Example
Let’s go back to the couple having five children.
Let X = # of children with type O blood.
p = P(success) = P(O blood) = 0.25
The possible values for X are what?
Using the binompdf(n,p,k) command, what is the
probability that the couple will have 1 child with
O blood?
Cumulative Distribution Function
The pdf command lets you find
probabilities for ONE value of X at a time.
The cdf command finds cumulative
probabilities. We can use it to quickly find
probabilities such as P(X < 7) or P(X ≥ 4).
The cdf will give you X ≤

Think of this like Table A
Using the Calculator
P(X=k)
Binompdf(n,p,k)
P(X<k)
Binomcdf(n,p,k-1)
P(X≤k)
Binomcdf(n,p,k)
P(X>k)
1-Binomcdf(n,p,k)
P(X≥k)
1-Binomcdf(n,p,k-1)
Batch’s Free Throws
Chris makes 75% of his free throws over
the course of a season. In a key game, he
shoots 12 free throws and makes 7 of
them. Is it unusual for him to shoot this
poorly?
What is the probability that Chris makes at
least 6 of the 12 free throws?
How many free throws would we expect
Chris to make?
The Mean and Standard Deviation of
a Binomial Random Variable
The mean of a binomial random variable is np.

This formula, while intuitive, is given to you on the AP
Exam.
The standard deviation of a binomial random
variable is
np(1  p) This formula is also given to you.
What is the standard deviation for the number of
free throws Chris is expected to make?
The Mean and Standard Deviation
of a Binomial Random Variable
Expected value of X is the same as
_____________ of X.
Let’s go back to the couple having five
children. Let X = # of children with type O
blood. p = P(success) = P(O blood) = 0.25
What is the expected number of children
with type O blood?
What is the standard deviation?
How the AP folks force you to use the
formula
In a carnival game, a person can win a prize by guessing
which one of 5 identical boxes contains the prize. If a
person makes 4 guesses, what is the probability that the
person wins a prize exactly 2 times?
2!
A)
5!
(0.2) 2
D)
(0.8) 2
B) 2(0.2)(0.8)
 4
E)   (0.2) 2 (0.8) 2
 2
C) (0.2) 2 (0.8) 2
And yet another way…
What is the mean of the random variable X if
10 
k
10  k
P( X  k )    (0.3) (0.7)
k 