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Normal Distribution

Normal Distribution. Symmetrical Continuous Unimodal Mean= Median = Mode Asymptotic Tail Almost 100% of scores fits between -3 and +3 stdev from the mean . How to Determine if Nearly Normal. Unimodal Relatively Symmetric. Are Bobsled times Nearly Normal?. NO. Is it nearly normal?.

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Normal Distribution

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  1. Normal Distribution Symmetrical Continuous Unimodal Mean= Median = Mode Asymptotic Tail Almost 100% of scores fits between -3 and +3 stdev from the mean

  2. How to Determine if Nearly Normal Unimodal Relatively Symmetric

  3. Are Bobsled times Nearly Normal? NO

  4. Is it nearly normal? YES

  5. Shot Put 100 Meter Dash Long Jump Who won? Shot Put 100 m DashLong Jump Ashton Eaton 66’: 1st10 sec 26’ Trey Hardee 60’ 9.8 sec: 1st 26.25’ Leonel Suarez63’ 10.6 sec 27.5’: 1st

  6. Evaluate the relative location of each person on the event’s normal curve Shot Put 100 m Dash Long Jump • + z score = right of the mean • z score = left of the mean • Can compare z scores from different distributions

  7. Standard Scores: Z score • + z score = right of the mean • z score = left of the mean • Can compare z scores from different distributions

  8. z-score looks at one data point, x, and tells us how many standard deviations x is from the mean. You need to know this for the quiz Z =1 68% of all data points are within 1 stdev.of the mean Z =2 95% are within 2 stdev. of the mean Z =3 99.7% are within 3 stdev. of the mean

  9. 100 m Dash Shot Put Long Jump Ashton Eaton 10 sec 66’ 26’ Trey Hardee 9.8 sec 60’ 26.25’ Leonel Suarez10.6 sec 63’ 27.5’ Z = 0 Z= 1 Z= -3 Z = 2 Z= 0 Z= 1 Z = 0 Z= 0.5 Z= 3 Mean 10 sec 60’ 26’ St Dev.2 sec 3’ 0.5’

  10. How to use the z-scoreWatch & Listen…

  11. IQ scores have the distribution: N(100,16), What is the probability of having a score less than 132?Two ways to computer probability: 1) z-scoresand z-table: A- 56 & A-572) 68 – 95 – 97.5 rule (only works when z score is ±1, ±2, or ±3)

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