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HW-pg. 524 (8.14-8.17) & pg. 529-530 (8.21-8.24)
8.1 Quiz Monday 1-7-13 Ch. 8 Test Friday 1-11-13
www.westex.org HS, Teacher Website
1-3-12
Warm up—AP Stats
A coin is flipped 25 times. Let X represent the
number of heads. We assume X has a binomial
distribution. What is the probability of getting 7 or
less heads in the 25 flips?
Name _________________________
AP Stats
8 The Binomial and Geometric Distributions
8.1 The Binomial Distributions (Day 2)
Date _______
Objectives
 Explain the difference between binompdf (n,p,X) and binomcdf (n,p,X).
 Use your CALCULATOR to help evaluate a binomial probability.
 If X is B(n, p), find  X and  X .

Use a Normal approximation for a binomial distribution to solve questions involving
binomial probability.
In practice you will rarely have to use the formula for calculating the probability that a binomial
random variable takes any (or a range as in the warm up) of its values. Our calculator can do
the heavy lifting of calculating ____________ _______________.
Probability Distribution Function (pdf)
Given a discrete random variable X, the _______________ _______________ __________
(pdf) assigns probability to EACH value of X.
So let’s look at a variation from the warm up question.
Ex. A coin is flipped 25 times. Let X represent the number of heads. We assume X has a
binomial distribution. What is the probability of getting exactly 7 heads in the 25 flips?
Frequently, like in the original warm up question, we want to find the probability that a random
variable takes a __________ of values.
Cumulative Distribution Function (cdf)
Given a random variable X, the _______________ ______________ ___________ (cdf) of
X calculates the SUM of the probabilities for 0, 1, 2, . . ., up to the value X. In other words it
calculates the probability of obtaining ___ _______ ___ successes in n trials.
Ex. A coin is flipped 25 times. Let X represent the number of heads. We assume X has a
binomial distribution. What is the probability of getting 7 or less heads in the 25 flips?
Exercise 8.13 Inherited blood type continued-Each child is born to a particular set of parents
and has probability 0.25 of having type O blood. Suppose these parents have 5 children.
Let X = number of children who have type O blood. Then X is B(5, 0.25).
Make a table for the pdf and cdf of the random variable X.
Binomial Mean and Standard Deviation
If a count X has the binomial distribution based on n observations with probability p of success,
what is its mean µ ? Think back to yesterday’s warm up with Joe taking 75 free throws and
averaging making 60% of his free throw shots for the year. Wouldn’t we expect him to make
_____ shots which is calculated by multiplying his __________ by his _______________?
Mean and Standard Deviation of a Binomial Random Variable
If a count X has the binomial distribution with number of observations n and probability of
success p, the mean and standard deviation of X are:
µ = _____
σ = _______________
***These formulas are ONLY for binomial distributions. They can’t be used for other
____________ random variables.***
The derivation of the standard deviation is on pg. 525. Check it out when you are bored!
Example 8.11-Bad Switches
Continuing from an earlier example, the count X of bad switches is binomial with n = 10 and
p = 0.1. What are the mean and standard deviation of the binomial distribution?
Believe it or not, a discrete probability distribution (a binomial probability distribution) can be
reliably approximated by a continuous probability distribution (a Normal distribution) when n is
large.
The Normal Approximation to Binomial Distributions
As the number of trials n gets __________, the binomial distribution gets ________ to a
Normal distribution. As a result we can use Normal probability calculations to approximate
binomial probabilities.
Do example 8.12 below as a binomial distribution and then as a Normal approximation to a
binomial distribution.
Example 8.12-Attitudes toward shopping
Are attitudes toward shopping changing? Sample surveys show that fewer people enjoy
shopping than in the past. A survey asked a nationwide random sample of 2500 adults if they
agreed or disagreed that “I like buying new clothes, but shopping is often frustrating and timeconsuming.” The population that the poll wants to draw conclusions about is all U.S. residents
aged 18 and over. Suppose that in fact 60% of all adult U.S. residents would “Agree” if asked
the same question. What is the probability that 1520 or more of the sample agree?
Normal Approximation for Binomial Distributions
Suppose that a count X has the binomial distribution with n trials and success probability p.
When n is large, the distribution of X is approximately Normal, N(np, np(1  p) ). As a rule of
thumb, we will use the Normal approximation when n and p satisfy np  10 and n(1 – p)  10.
***Accuracy of the Normal approximation improves as the sample size n ____________ and
when p is close to ½.***
Whether or not you use the Normal approximation should depend on how accurate your
calculations need to be. In statistics usually great accuracy is not required.