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.