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Z Scores & Normal Curves

Notes #3. Z Scores & Normal Curves. What are Z-Scores?. ANS Determines how many standard deviations a raw score is from the mean. The Z-score can be used to determine the probability of an event occurring. 2 Types of Z-Scores. 1 .Positive z - score , the data value lies

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Z Scores & Normal Curves

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  1. Notes #3 Z Scores & Normal Curves

  2. What are Z-Scores? ANS • Determines how many standard deviations a raw score is from the mean. • The Z-score can be used to determine the probabilityof an event occurring.

  3. 2 Types of Z-Scores 1.Positive z-score, the data value lies abovethe mean 2. Negativez-score, the data value lies below the mean.

  4. Z-Score Formula: Symbols: x : Raw score or number in question m : Mean of the data set s : Standard Deviation of the data set

  5. Example 1 What is the z score for Iowa test score of 3.74, with a mean of 6.84 and standard deviation of 1.55? z = (3.74 – 6.84)/1.55 z = -2 FINAL ANS: This says that a score of 3.74 is 2 standard deviation BELOW the mean

  6. Ex. 2: Comparing the z-score data • A set of math test scores has a mean of 70 and a standard deviation of 8. • A set of English test scores has a mean • of 74 and a standard deviation of 16. For which test would a score of 78 have a higher standing?

  7. Analyzing the data To solve: Find the z-score for each test. ANS: The score of 78 on the math test has a higher standing since it is 1 standard deviation above the mean. While a score of the 78 on the English score is only .25 standard deviation above the mean.

  8. Ex. 3: Using Z-score to determine raw score What will be the miles per gallon for a Toyota Camry when the average mpg is 23, it has a z value of 1.5 and a standard deviation of 5? Using the formula for z-scores: Step 2 Step 3 Step 1 ANS: The Toyota Camry would be expected to use 30.5 mpg of gasoline.

  9. Suppose SAT scores among college students are normally distributed with a mean of 500 and a standard deviation of 100. If a student scores a 700, what would be her z-score?

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