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