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A young athlete runs the 400 meter dash and records his trials in seconds. Find the mean and standard deviation for the data from his sprints: 50.6, 50.9, 49.1, 51.3, 50.5, 49.7, 51.5, 49.8, 51.1, 48.9, 50.3, 49.2, 51.2, 50.4, 52.8. Today you will be able to: Calculate the mean Calculate the mode Calculate the median Calculate the range, and IQR Calculate the variance Calculate the standard deviation Do a statistical analysis and compare data sets Use your calculator to run an analysis Identify measures of center Identify measure of variability Label the percentage intervals of a normal distribution Determine probability using empirical rule 68-95-99.7 Determine probability using z-scores Standard Normal Distributions May 24, 2017 Empirical Rule Main Entry: em·pir·i·cal Function: adjective Date: 1569 1 : originating in or based on observation or experience <empirical data> 2 : relying on experience or observation alone often without due regard for system and theory <an empirical basis for the theory> 3 : capable of being verified or disproved by observation or experiment <empirical laws> about 68% of a data set lies in the range X to X about 95% of a data set lies in the range X 2 to X 2 X 3 to X 3 almost all of a data set lies in the range 34% of your data 34% of your data 13.5% of your data 2.35% of your data 13.5% of your data 2.35% of your data 0.15% of your data 0.15% of your data x Normal Distribution: A bell-shaped, normal curve that is symmetric about the mean; total area under the curve is 1 34% of your data 34% of your data 13.5% of your data 2.35% of your data 13.5% of your data 2.35% of your data 0.15% of your data 0.15% of your data x Standard Normal Distribution A normal distribution has a mean and a standard deviation. Find the indicated probability for a randomly selected x-value from the distribution. 1.) 3.) P( X x X 2 ) P( x X ) 2.) P( x X ) 4.) P( X x X ) Give the percent of the area under the normal curve represented by the shaded region. x Standard Normal Distribution Your Turn… A normal distribution has a mean of 27 and a standard deviation of 5. • a.) Find the probability that a randomly selected value will be between 22 and 32. • b.) Find the probability that a randomly selected value will be between 12 and 27. • c.) Find the probability that a randomly selected value will be between 17 and 37. • d.) Find the probability that a randomly selected value will be at least 22. A young athlete runs the 800 meter dash and records his trials in seconds. Find the mean and standard deviation for the data from his sprints: 50.6, 50.9, 49.1, 51.3, 50.5, 49.7, 51.5, 49.8, 51.1, 48.9, 50.3, 49.2, 51.2, 50.4, 52.8. Interval X to X Numerical Interval Fraction of data in interval Empirical Rule 68% X 2 to X 2 95% X 3 to X 3 99.7% z X X Normal Score of x Today you will be able to: Calculate the mean Calculate the mode Calculate the median Calculate the range, and IQR Calculate the variance Calculate the standard deviation Do a statistical analysis and compare data sets Use your calculator to run an analysis Identify measures of center Identify measure of variability Label the percentage intervals of a normal distribution Determine probability using empirical rule 68-95-99.7 Determine probability using z-scores