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Z-Score Practice Worksheet 1. A normal distribution of scores has a standard rd deviation of 10. Find the z-scores corresponding to each of the following values: a) A score that is 30 points above the mean. b) A score that is 20 points below the mean. c) A score that is 25 points above the mean d) A score that is 10 points below the mean. 2. The Welcher Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of 35 and a standard deviation of 6. Assuming these raw scores form a normal distribution: a) What number represents the 75th percentile (what number separates the lower 75% of the distribution)? b) What number represents the 80th percentile? c) What is the probability of getting a raw score between 26 and 36? d) What is the probability of getting a raw score between 31 and 41? 3. Scores on the SAT form a normal distribution with u = 500 and o = 100. a) What is the minimum score necessary to be in the top 25% of the SAT distribution? b) Find the range of values that defines the middle 80% of the distribution of SAT scores. 4. For a normal distribution, find the z-score that separates the distribution as follows: a) Separate the highest 20% from the rest of the distribution. b) Separate the lowest 30% from the rest of the distribution. c) Separate the highest 85% from the rest of the distribution. 5. For the numbers below, find the area between the mean and the z-score: a) z= 1.27 b ) z = - 1.47