normal 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

The Normal Distribution Curve standard deviation standard deviation standard deviation mean

68% of the data falls within 1 standard deviation

68% of the data falls within 2 standard deviations 95%

68% of the data falls within 3 standard deviations 99.7%

When you break it up… (copy this!!) 34% 34% .15% .15% 13.5% 13.5% 2.35% 2.35% mean mean - 1SD mean + 1SD mean + 3SD mean - 3SD mean - 2SD mean + 2SD

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.

Example 1 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. Set up a normal distribution curve.

Example 2 a) What percentage of operations last at least 125 minutes? 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. Set up a normal distribution curve.

Example 3 Determine how many of the 850 students weigh: **This question is not asking for percents! Between 64 kg and 73 kg. More than 76 kg. Less than 67 kg. Between 70 kg and 76 kg.