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Normal Distributions & z score

Normal Distributions & z score. Dec. 9. Normal Distribution. Tend to cluster around the mean Symmetrical bell-shaped frequency polygon Mode, median, mean all occur at the highest point, in the center of distribution

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Normal Distributions & z score

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  1. Normal Distributions & z score Dec. 9

  2. Normal Distribution • Tend to cluster around the mean • Symmetrical • bell-shaped frequency polygon • Mode, median, mean all occur at the highest point, in the center of distribution • 3 units of SD to the left of the mean and 3 units of SD to the right of the mean • 99.74% of polygon area lies btw –3SD and +3SD

  3. Skewed Distribution • A large percentage the values is on either left or right side • Positively skewed • Has a tail to the right • Negatively skewed • Has a tail to the left

  4. z scores • Used to compare values of interval or ratio –level variables • Rita’s score of 21 out of 24 vs. Mary’s score 85 out of 100 • Variables should be normally distributed • z score equals raw score minus mean divided by SD • Can be converted to percentiles • Known as standard scores

  5. Areas of Normal Curve Table

  6. Examples of z Scores & corresponding Areas and percentiles

  7. Exercise • On an IQ test with a mean of 100, SD of 16, what is the percentile of IQ 104?

  8. Debora leads a treatment group of college students diagnosed as chronic anxiety. Group members have been selected for treatment on the basis their scores on Anxiety Scale A with a mean of 70 and SD of 10 or Scale B with mean of 50 and SD of 12. Gina had score of 78 on the Scale A and Tom received 66 on the Scale B. There is only one vacancy in the group. Who should be in the treatment group?

  9. Deriving Raw Scores from Percentiles • Lauren wishes to form a treatment group of college students with high anxiety levels using the results of testing with Scale B (mean=50, SD=12). She wants to include the top 10% of all students measured by Scale B. What is the cutoff point?

  10. Subtract the percentile of mean (50) from 90 to determine the area of a normal curve that would fall between the 90th percentile and the mean • Find the z score corresponding to the area • Use the z score formula, add 50 if the z score is positive

  11. Exercise One hundred students took mid-term exam designed to measure knowledge of statistics. Their scores on it formed a normal distribution with a mean of 80 and a standard deviation of 6. Instructor decided to assign A to the top 10% of the scores. What score does John have to get to earn?

  12. Exercise • 89,56,45,78,98,45,55,77,88,99,98,97,54,34,94 • 77,88,87,67,98,87,55,77,45,44,88,99,69,67,98 • Calculate the mode, median, mean, range, variance, and standard deviation for both sections. Which section did better overall on the exam?

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