1. Chapter 5 The Binomial Probability Distribution and Related Topics

2. Essential Question: How are the mean and the standard deviation determined from a discrete probability distribution?

3. Student Objectives: The student will distinguish between random and discrete random variables. The student will graph discrete probability distributions. The student will compute the mean and standard deviation for a discrete probability distribution. The student will compute the mean and standard deviation for a linear function of a random variable x. The student will compute the mean and standard deviation for a linear combination of two independent random variables.

4. Terms: Continuous random variable Discrete random variable Linear function of a random variable Linear function of two independent random variables Mean Probability Distribution Random variable Standard deviation

5. Statistical Experiment any process by which an observation (or measurement) is obtained

6. Examples of Statistical Experiments Counting the number of books in the College Library Counting the number of mistakes on a page of text Measuring the amount of rainfall in your state during the month of June

7. Random Variable a quantitative variable that assumes a value determined by chance

8. Discrete Random Variable A discrete random variable is a quantitative random variable that can take on only a finite number of values or a countable number of values. Example: the number of books in the College Library

9. Continuous Random Variable A continuous random variable is a quantitative random variable that can take on any of the countless number of values in a line interval or a measurable amount. Example: the amount of rainfall in your state during the month of June

10. Continuous vs Discrete Directions: In problems #1 - 7, identify each of the following as either a discrete or continuous random variable. 1.The number of people who are in a car. 2.The number of miles you drive in one week. 3.The weight of a box of cereal. 4.The number of boxes of cereal you buy in one year. 5.The length of time you spend eating your lunch. 6.The number of patients on a psychiatric ward in one day. 7.The volume of blood that is transfused during an operation. Continuous Discrete Continuous Discrete Continuous Discrete

11. Probability Distribution an assignment of probabilities to the specific values of the random variable or to a range of values of the random variable

12. Probability Distribution of a Discrete Random Variable A probability is assigned to each value of the random variable. The sum of these probabilities must be 1.

13. Probability distribution for the rolling of an ordinary fair die

14. Features of a Probability Distribution Probabilities must be between zero and one (inclusive) Σ P(x) =1

16. Mean and standard deviation of a discrete probability distribution Mean =  = expectation or expected value, the long-run average Formula :

17. Standard Deviation

18. Finding the mean:

19. Finding the standard deviation

20. Standard Deviation

21. 8.In a personality inventory test for passive-aggressive traits, the possible scores are: 1 = extremely passive 2 = moderately passive 3 = neither 4 = moderately aggressive 5 = extremely aggressive The test was administered to a group of 110 people and the results were as follows: Construct a probability distribution table, calculate the expected value (the mean) and the standard deviation. Use a histogram to graph the probability distribution. x (score)12345 f (frequency)1923322610 xfP(x) 119 223 332 426 510 Sum: Probability Distributions

22. 8.The histogram: Probability Distributions

23. 8.The chart: Probability Distributions xfP(x)xP(x)x - µ(x - µ) 2 (x - µ) 2 P(x) 1190.1727 -1.86363.47310.5999 2230.20910.4182-0.86360.74590.1560 3320.29090.87270.13640.01860.0054 4260.23640.94551.13641.29130.3052 5100.09090.45452.13644.56400.4149 Sum:1101.00002.86361.4814 1 = extremely passive 2 = moderately passive 3 = neither 4 = moderately aggressive 5 = extremely aggressive

24. Linear Functions

25. Linear Combinations

26. 9. Linear Functions and Combinations a.

27. 9. Linear Functions and Combinations b.

28. 9. a. Linear Functions and Combinations

29. 9. a.

30. 9. Linear Functions and Combinations b.

31. Homework Assignment Chapter 5 Section 1 Pages 190 - 195 Exercises: #1 - 19, odd Exercises: # 2 - 18, even