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Density Curves A density curve - is always on or above the horizontal axis - has an area of exactly one We use different symbols for the mean and standard deviation of a density curve. mean - Examples of density curves standard deviation - Density Curves Example 1: The time that a person waits for the elevator by the bookroom is uniformly distributed with a mean of 1.5 minutes and a range of 1 minute. a. Construct a distribution for the above information. b. What percent of the observations would involve a wait time of less than 1.25 minutes? c. What percent of the observations would involve a wait time of between 1.2 and 2 minutes? Density Curves Example 2: Consider the population that consists of all soft contact lenses made by a particular manufacturer and define the variable x = thickness (in mm). Suppose that a reasonable model for the population distribution is the one shown below: a. Verify that the total area under the density curve is equal to 1. b. What percent of the contact lenses have thickness less than .20mm? Less than .10mm? c. What percent of the contact lenses are within .05 mm of the mean of thickness? The Normal Curve Symmetrical, single peaked, bell-shaped density curve Used for : SAT scores, heights, intelligence, etc. The Normal Curve Empirical Rule (or 68-95-99.7 rule) • Approximately 68% of the observations are Can ONLY be used within 1 of with normal curves! • Approximately 95% of the observations are within 2 of • Approximately 99.7% of the observations are within 3 of The Normal Curve Empirical Rule (or 68-95-99.7 rule) 68% 2.35% 2.35% 13.5% 34% 34% 0.15% 13.5% 0.15% 95% 99.7% The Normal Curve Example: page 133: #26