1 / 10

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

cobosa
Download Presentation

Z Scores & Normal Curves

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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?

More Related