A young athlete runs the 400 meter dash

Today you will be able to: q q q q Calculate the mean Calculate

Standard Normal Distributions 09 January 2022

Empirical Rule Main Entry: em·pir·i·cal Function: adjective Date: 1569 1 : originating in or

about 68% of a data set lies in the range about 95% of a

34% of your data 13. 5% of your data 2. 35% of your data

Give the percent of the area under the normal curve represented by the shaded

Your Turn… A normal distribution has a mean of 27 and a standard deviation

A young athlete runs the 800 meter dash and records his trials in seconds.

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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: q q q q 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 09 January 2022

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 theory> 3 : capable of being verified or disproved by observation or experiment <empirical laws>

about 68% of a data set lies in the range about 95% of a data set lies in the range almost all of a data set lies in the range 34% of your data 13. 5% of your data 2. 35% of your data 0. 15% of your data Normal Distribution: A bell-shaped, normal curve that is symmetric about the mean; total area under the curve is 1

34% of your data 13. 5% of your data 2. 35% of your data 0. 15% of your data 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. ) 2. ) 3. ) 4. )

Give the percent of the area under the normal curve represented by the shaded region. 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 Numerical Interval Fraction of data in interval Empirical Rule 68% 95% 99. 7%

Normal Score of x