Warm Up If there are 2000 students total in the school, what percentage of the students are in each section? 50 680 270.

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Normal Distributions & the Empirical Rule

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Warm Up If there are 2000 students total in the school, what percentage of the students are in each section? 50 680 270

Unit 8 Day 5 Normal Distribution

Distribution Shapes

Mean & Median

Normal Distribution Most common distribution in statistics Many real-life data sets follow this pattern Examples: SAT scores, heights of people, IQ tests Also known as a bell curve

Normal Distribution Mean, median and mode are all the same Symmetric with respect to the mean Highest point on the curve is the mean

Normal Distribution: COPY THIS! .15% 2.35% 13.5% 34% 34% 13.5% 2.35% .15%

Example 1: Suppose that patient’s systolic blood pressures follow a normal distribution with a mean of 108 and a standard deviation of 14. What percentage of patients have a blood pressure of 94 or higher? What percentage of patients have a blood pressure between 80 and 122? What percentage of patients have a blood pressure of less that 80?

Example 2: The duration of routine operations in a certain hospital has approximately a normal distribution with an average of 125 minutes and a standard deviation of 18 minutes. a) What percentage of operations last 125 minutes or more? b) What percentage of operations lasted between 107 and 143 minutes? c) What percentage of operations lasted between 89 and 125 minutes?

Example 3: The mean weight of 850 college students is 70 kg and the standard deviation of 3 kg. Assuming that the weight is normally distributed, determine how many students weigh: Between 64 kg and 73 kg. More than 76 kg. Less than 67 kg. Between 70 kg and 76 kg.