Z-score practice problems: A new Georgla HS aptitude test has scores are normally distributed with a mean of 100 and a standard deviation of 15. Let's use the normal curve to determine the probability of randomly selecting someone from the population with a score as high or higher than a certain amount. 1. EXAMPLE: You are a school school psychologist who wants to know the probability of selecting a student from the general population who has a score of at least 119 (Le, 119 or higher). a. cenvert iQ score to Z score (z X- mean)/std dev) Steps: 119-100/15 19/15 -z score of + 1.27 b. sketch out what you're looking for -> look up obtained value in z table 1.27: area between mean and z 3979 = 39.79% 1.27: area bevond z=0.1020 - 10.20% d. decision - probability of someone with IQ at least 119-.1020 2. Now, what is the probability of selecting a student with a score of 85 or higher? a. Convert b. Sketch C. Look up d. Decislon 3. Now, what is the probability of selecting a student with a score between 90 and 110? a. Convert b. Sketch C Look up d. Decision 4. Now, there is a new collegiate scholarship that requires a test score in the top 7%. The school psychologist wants to determine what the cut-off score is for nominating students. What is the (minimum) cut off score the top 7% of students (hint: sort of a backwards problem -- instead of solving for z, solve for X)? a. Convert b. Sketch C. Look up d. Decision

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