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9:23 4 4 Back Ch 5 z- scores -1.pdf Q Ch 5 z-scores: Location of Scores and Standardized Distribution 1. A distribution has a standard deviation of o = 10. Find the z- scores for each of the following locations in the distribution. a. Above the mean by 5 points. b. Above the mean by 2 points. c. Above the mean by 20 points. d. Above the mean by 15 points. 2. For a population with / = 80 and o = 10, a. Find the z-scores for each of the following X values. (Note: You should be able to find these values using the definition of a z-scores. You should not need to use a formula or do any serious calculations.) X= 75 X= 100 X= 60 X= 95 X= 50 X= 85 3. For a population with a mean of u = 100 and a standard deviation of o = 20. a. Find the z-scores for each of the following X values. X= 108 X= 115 X= 130 X= 90 X= 88 X= 95 b. Find the score (X value) that corresponds to each of the following z- scores. X= -0.40 X= -0.50 X= 1.80 X= 0.75 X= 1.50 X= -1.25 4. A score that is 6 points below the mean corresponds to a z- score of z= -2.00. What is the population standard deviation? 5. For a population with a standard deviation of o = 12, a score of X = 44 corresponds to z = -0.50. What is the population mean? 6. For a sample with a mean of M = 51, a score of X= 59 corresponds to z = 2.00. What is the sample standard deviation? 7. In population distribution, a score of X= 28 corresponds to z= -1.00 and a score of X= 34 corresponds to z= -0.50. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.) 8. For each of the following populations, would a score of X= 50 be considered a. central score (near the middle of the distribution) or an extreme score (far out in the tail of the distribution)? a. u = 45 and o = 10 b. M = 45 and o = 2 C. M = 90 and o = 20 d. M = 60 and o = 20 9. A distribution of exam scores has a mean of u = 78. a. If your score is X= 70, which standard deviation would give you a better grade: o = 4 or 0 = 8? b. If your score is X= 80, which standard deviation would give you a better grade: o = 4 or 0 = 8? 0= 5 OOO Dashboard Calendar To Do Notifications Inbox