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

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

Natural Distribution

Distribution Shapes

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

Example The mean value of homes on a street is $125,000 with a standard deviation of $5,000. The data set has a bell shaped distribtion. Estimate the percent of homes between $120,000 and $130,000.

Example Suppose the class average on a test is 87% and the standard deviation of the class is 3. Find: The percentage of students who scored greater than 90%. The percentage of students who scored between 84% and 90%. The percentage of students who scored less than 84%. 16% 68% 16%

Example 1 Suppose that the average blood pressures of patients in a hospital follow a normal distribution with a mean of 108 and a standard deviation of 14. Set up a normal distribution curve. 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 mean weight of 850 college students is 70 kg and the standard deviation of 3 kg. Set up a normal distribution curve. 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.