1. Probability and Statistics

2. Probability Experimental Probability Sample Space
P(event)=number of times the event occurs
number of trials
Sample Space
Sample Space
Event

3. Events Independent Dependent Mutually Exclusive
When the outcome of one event does NOT effect the outcome of a second event
Dependent
When the outcome of one event affects the outcome of a second event
Mutually Exclusive
When two events cannot happen at the same time

4. Probability Probability of A and B If A and B are independent
P(A and B)= P(A)*P(B)
Probability of A or B
If mutually exclusive
P(A or B)= P(A) + P(B)
If NOT mutually exclusive
P(A or B)= P(A) + P(B)- P(A and B)

5. Probability Distributions
Frequency table is a list of the outcomes in a sample space and the number of times each occurs
Probability Distribution is a function that gives the probability of each event in a sample space

6. Conditional Probability
Contains a condition that may limit the sample space fro an event
Notation: P(B|A)
The probability of event B given event A
P(B|A)=

7. Homework Problems Practice 1-6 Practice 9-7 Practice 12-1
# 2, 3
Practice 9-7
# 1-8, 11, 14, 17
Practice 12-1
# 1, 2
Practice 12-2
# 2, 5

8. Probability and Analyzing Data

9. Counting Principle Used when a number of objects are being chosen
Multiply all possible choices together
Ex: Sally has 4 shirts, 12 pants, and 13 pairs of choose to choose from. How many outfits can be created?
4*12*13

10. Permutations and Combinations
Order matters with Permutations
Order does not matter with combinations
Permutations
nPr
Combinations
nCr

11. Examples
Seven yachts enter a race. First, second, and third places will be given to the three fastest yachts. How many arrangements of first, second, and third places are possible with seven yachts?
A reading list for a course in literature has 20 books on it. In how many ways can you choose four books to read?

12. Homework Reteaching 6-7 Practice 6-7 # 4-7
# 1-4, 10, 11, 12, 13, 16, 25, 27

13. Analyzing Data

14. Measures of Center Mean Median Mode
Average of all values in the data set
Median
Middle value when data set is in numerical order
If the data set has an even number of values then average the two middle terms
Mode
Most frequent value in the data set

15. Measures of center Put your data set in L1
Use 1-Var Statistics under stat, calc

16. Measures of Spread Range Standard Deviation Inter Quartile Range (IQR)
Maximum value- minimum value
Standard Deviation
σx in 1-var stats
Inter Quartile Range (IQR)
Q3-Q1

17. Quartiles Divides the data set into four equal parts
Q1- median of lower half of the data set
Q2- median of the data set
Q3- median of upper half of the data set

18. Displaying Data Box and Whisker Plots
Uses minimum, Q1, Q2, Q3, and maximum to create a box and whisker plot
These can also be graphed in the calculator under stat plot

19. Percentiles Divides the data set into two parts
One part above the percentile and one part below
Ex: If a number is at the 63rd percentile then about 63% of the data is below this number

20. Using Percentiles Example
54, 98, 45, 87, 98, 64, 21, 61, 71, 82, 93, 65, 62, 98, 87, 24, 65, 91, 31, 47
Order the data set 1st!
21, 24, 31, 45, 47, 54, 61, 62, 64, 65, 65, 71, 82, 87, 87, 93, 97, 98, 98, 98
Find the values of the 20th and 65th percentile (n=20)
20*.20= *.65=13
47 is the 20th percentile 87 is the 65th percentile

21. Finding Outliers
Outliers are values in the data set that are substantially different than the rest of the data set
To find outliers: 1. Calculate IQR
2. Multiply IQR times 1.5
3. Subtract the value from step 2 from Q1
4. Add the value from step 2 to Q3
Any values in the data set below or above step 3 and 4 are outliers!

22. Example
56, 65, 73, 59, 98, 65, 59
IQR= = 14
1.5(14) = 21
59-21 = 38
73+21 = 94
Any number below 38 or above 94 is an outlier….so 98 is an outlier

23. Homework Practice 12-3 Practice 12-4 # 1, 3, 5, 7, 22, 27, 29
# 1, 10, 15 parts a-d

24. Working with Samples

25. Recall Sample is a portion of a population
Samples can be bias based on who and where people are asked
A sample can be used to find a sample proportion
A ratio of the number of times an event occurs in a sample size of n

26. Choosing a sample
If every member of the population is equally likely to be chosen then it is a random sample
The larger the sample the smaller margin of error
A margin of error is calculated by

27. Homework
Practice 12-5
# 2 - 7, 11, 13

28. Binominal Distribution

29. Binominal Experiment Situation involves repeated trials
Each trial has two possible outcomes
Success or failure
The probability of success is constant throughout the trials
The trials are independent
Tree diagrams are used to analyze binominal probabilities

30. Binominal Probability
If there are repeated independent trials each with a probability of success, p, and a probability of failure, q. Then the probability of x successes in n trials is…

31. Example
A calculator contains four batteries. With normal use each batteries has a 90% chance of least 1 year. What is the probability that all four batteries will last a year?
n=4 x=4
p=.9 q=.1

32. Homework
Practice 12-6
# 3, #5 -8

33. Normal Distributions

34. Normal Distributions Shows data that vary randomly from the mean
The pattern of data is bell shaped
This is called a normal curve
Standard Normal Curve
A normal distribution centered on the y-axis
Mean = 0
Standard Deviation = 1

35. 68% -95%- 99.7% When the data set is normally distributed…
68% of the data falls within 1 standard deviation from the mean
95% of the data falls within 2 standard deviations from the mean
99.7% of the data falls within 3 standard deviations from the mean

36. Homework
Practice 12-7
# 5, 6 ,11, 12, 13, 16