1. Lecture 9: Basic Probability 2011, 10, 11

2. Today ’ s Topics 1.Review the Normal Distribution 2.How to use the Unit Normal Table?** 3.What is probability?

3. Properties of The Normal Distribution 1.Shape: Symmetrical and unimodal 2.Mean: μ = 0 3.The 68% -- 95% -- 99.7% rule

4. How to Transform Raw Scores into Proportions (or Percentages)  When the Stanford-Binet “IQ test” came into use in 1932, it was adjusted so that scores for each age group of children followed roughly the normal distribution with mean  = 100 and standard deviation  = 15. IQ scores above 122.5 are often called “very superior.” What percent of children has very superior scores?  What percent of children has an IQ score at or lower than 80?  What percent of children has an IQ score between 80 and 122.5?

5. Your Turn

6. How Transform Proportions (or Percentages) into Raw Scores The GRE Verbal test is normally distributed with  = 470 and  = 120. If the graduate program you want to apply only take the top 5% applicants. To be accepted, what GRE verbal score you must have?The GRE Verbal test is normally distributed with  = 470 and  = 120. If the graduate program you want to apply only take the top 5% applicants. To be accepted, what GRE verbal score you must have? A student took the on-line GRE test. He was told that 45% students scored below him. What is his raw score?A student took the on-line GRE test. He was told that 45% students scored below him. What is his raw score?

7. Your Turn

8. Probability  Rolling a dice. A die has six sides. The probability that dice rolling results in “ 1 ” is …  p(1) = 1/6 =.17  Probability refers to the long run relative frequency of a certain event(s). Total number of possible outcomes Total number of outcomes classified as A Prob. of A = p(A) =

9. Probability  A basketball player shoots four free throws. You record the sequence of hits and misses. –Write out all 16 arrangements of the four throws (e.g., YYNY). –What is the probability of hitting all four free throws? –what is the probability of hitting at least 3 free throws?

10. Probability  What is the probability of picking up a yellow M&M?  What is the probability of drawing out a blue M&M? –All possible outcomes together have a probability equal to 1.0  What is the probability that a M&M is any of red, yellow, or orange? –If two events have no common outcomes, then the probability that one or the other occurs is the sum of their individual probabilities/ Color Brown Red Yellow Green Orange Blue Probability 0.3 0.2 0.2 0.1 0.1 ??

11. Lecture 9 Recap  The Normal Distribution –How to use the Unit Normal Table to find out the percentage for a raw score? –How to use the Unit Normal Table to find out the raw score for a percentage?  How to calculate the probability of an event?