AP Statistics: Chapter 8 Intro.

You come to class totally unprepared for a quiz (imagine that!!!). The quiz consists of

10 multiple choice questions with 5 possible answers. Since you are completely

unprepared, you simply randomly fill in answers on the Scan Tron sheet without

even reading the questions.

Do this at the right.

What is P(get a particular question correct) = _______

How many questions would you expect to get correct? _______

51

2

Let the random variable X represent the number of questions you get correct and complete this

probability distribution.

To find the probabilities, let’s do a simulation:

Each of you do 10 simulations.

PRB MATH

.ALPHA

MATH 2nd MATH STAT 2nd

0 1 2 3 4 5 6 7 8 9 10

We can also find these probabilities theoretically.

P(0) is fairly straight forward. ___________1074.)8(. 10

For the P(1), P(2), etc., we need to consider all the different ways we can 1 correct or two

correct, etc.

To determine the number of ways of arranging k successes in n observations we can use the

following formula:

TI83/84: MATH PRB 4:!

8!=

40320

TI83/84: MATH PRB 3: nCr

(note: put in n, then do nCr then put in r)

10110 nCr

P(1) = ___________________

P(2) = ___________________ P(3) = ___________________

P(4) = ___________________ P(5) = ___________________

2684.8.2.10 91

3019.8.2.45 82

2013.8.2.120 73

0881.8.2.210 64

0264.8.2.252 55

If you need 60% to pass the quiz, what is P(at least 6 questions

correct)?

0065.0264.0881.2013.3019.2684.1074.1

Probabilities such as these can be found very easily using the

BINOMIAL Distribution.