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Probability Chapter 6 (part 4) 4. Example: It is known that IQ scores form a normal distribution with μ=100 and σ=15. What is the probability of randomly selecting an individual with an IQ score less than 130? 4. Example Contd. Given μ=100 and σ=15 what is p (X<130)=? First Step: Sketch the distribution and locate the score and the shade the area you are interested in. Second Step: Change X value to Z score. z=(X-μ)/σ = (130-100)/15 = +2.00 Third Step: Look up z-score value in Unit Normal table for are of interest, in this case the body, z score of +2.00 corresponds to a proportion of 0.9772 so: p (X<130)=0.9772 (or 97.72%) 5. Looking ahead to Inferential Statistics A diagram of a research study. A sample is selected from the population and receives a treatment. The goal is to determine whether or not the treatment has an effect. 5. Looking ahead to Inferential Statistics Boundaries provide the deciding criteria. Boundaries provide the deciding criteria. Using probability to evaluate a treatment effect. Values that are extremely unlikely to be obtained from the original population are viewed as evidence of a treatment effect. Class Exercise-1 If a vertical line is drawn through a normal distribution at each of the following zscore locations, then determine whether the tail is on the left side or the right side of the line and determine what proportion of the distribution is located in the tail: z=+1.00, z=+0.50, z=-1.50, z=-2.00 Class Exercise-2 For a normal distribution, find the z-score location of a line that would separate the distribution as described in each of the following: a. Where should the line be drawn to separate the top 5% from the rest? b. Where should the line be drawn to separate the top 20% from the rest? c. Where should the line be drawn to separate the bottom 40% from the rest? Class Exercise-3 A normal distribution has a mean of μ=61 with a σ=8. Find the following probabilities: a. p (X<55) b. p (X<70) c. p (51<X<73)