7.5 The Binomial Distribution -- Graphing Calculator Version

[Pages:2]7.5 The Binomial Distribution -- Graphing Calculator Version

1. Review Example: If the chance to jump a tomato is 20%, find the probability that in 10 people, exactly 2 make it over.

Answer: So

n = 10, p = 0.2, x = 2.

P(x 2) 10C2 .22 .88

P(x 2) 45.22 .88

P(x) nCx px 1 p nx

P(x 2) .3020 Try this! Make sure you can do this. We'll use this example throughout the notes.

2. Graphing Calculator!

The graphing calculator can do all this for you! But it's only for checking your answer.

Go to 2nd vars (distr) and then down to A. ----------------------------------------------------------------------------------------------a) To find P(X = 2):

binompdf(10, 0.2, 2) it goes alphabetical, n, p, x.

This is the probability of two successes. Try this! Did you get .3020 like above? ----------------------------------------------------------------------------------------------b) To find P(X 2):

binomcdf(10,0.2, 2) cdf, not pdf!

That's the probability from 2 down, with 2 included. Try this! Did you get .6778? This is P(X = 0) + P(X = 1) + P(X = 2).

What work to show? Do it in the calculator but show only the first one and the last one, like this:

For example, P(x 5) = 10C0 .20 .810 + ... + 10C5 .25 .85

------------------------------------------------------------------------------------------------c) To find P(X 2):

You need to do 1 ? P(X 1). Try this! Did you get .6242?

3. Another cool calculator thing

Here is the whole probability distribution for the tomato jumping example.

x 0 1 2 3 4 5 6 7 8 9 10 p .107 .268 .302 .201 .088 .026 .006 .001 .000 .000 .000

So for example, the probability of 4 people jumping a tomato out of 10 is .088.

Try this: binompdf(10, 0.2) Then scroll to the right with your right arrow button. So if you don't put in an "x" it gives you the whole probability distribution! Try this! Did you get the whole table above?

4. The Mean and Standard Deviation

How to find the mean number of people who can jump. -------------------------------------------

Method 1: xp = (0)(.107) + (1)(.268) + (2)(.302) + ... + (10)(.000) = 2 people

Method 2: Shortcut! np ! Try this using the short formula above! Did you get 2 people?

--------------------------------------------

How to find the standard deviation of the number of people who can jump. -------------------------------------------

Method 1:

x 2 p = (0 4)2 (.107) ... (10 4)2 (.000) 1.2649

Method 2: Shortcut! np(1 p) !

Try this using the short formula above! Did you get 1.2649 people? -------------------------------------------

To summarize, here are the shortcut formulas for the mean and standard deviation of a binomial:

np and np(1 p)

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download