6.2 The Binomial Distribution
Reading Guide
Binomial Probabilities
Many random variables seen in practice amount to ______in n ______trials. These situations are called ______because each trial has ______possible outcomes.
Jack and Jill were asking questions about a ______when they wanted to know the answer to a question like, “______
______, what is the probability that ______?”
We got a list of ______possible outcomes, all ______if none of the four can tell the difference and they are ______. Using the ______, we know that the probability of getting a particular outcome when two people guess correctly, say, CIIC, is ______. There are _ where two people guess correctly. So the probability of getting two people who correctly select tap water is ____.
The number of ways we can choose exactly 2 people out of 4 people to identify the tap water is
Example: College Graduates
The proportion of adults age 25 or older in the US with at least a bachelor’s degree is ______. Suppose you pick 7 adults at random. What is the probability that ______will have a bachelor’s degree or higher?
All that matters to determine the probability is that the adults were ______selected and the ______stays the same. For example, one outcome with three grads is
By the ______the probability for this particular outcome is
Another outcome for 3 grads is
The probability for this particular outcome is
Which is ______the same.
That’s because the probabilities of outcomes with ______all have the same factors but in different ______.
There are ___ of them because
So the probability for getting exactly three college grads is
(______)∙(______)
or ______
You may have noticed that the trials in Jack and Jill’s example aren’t really ______. The first adult selected who was ______has a ______of being a college graduate. If that person is a college graduate, the probability of the next person selected is a college graduate is ______. However the change in probability is ______, that Jack and Jill can ______.
You can treat your random sample as a ______as long as the sample size, n is ______compared to the population size, ____. A simple guideline that works well in practice is the ___ should be less than ____ of the size of the population, or ______.
Shape, Center and Spread of a Binomial Distribution
The fact that the ______is represented by such a simple and elegant ______might lead you to believe that there is a simple ______for the ______and ______as well.
As p comes closer to ______the distribution looks approximately normal.
As n increases, the distribution looks closer to ______.
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