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Math 20-2 Statistics: Lesson #4 The Normal Distribution Objective: By the end of the lesson, you should be able to: - Explain the properties of a normal curve, including the mean, median, mode, standard deviation, and area under the curve. - Determine if a data set approximates a normal distribution. Key Point: One of the most important and frequently occurring statistical distributions is the normal distribution. If the sample studied is large enough, many measurements in real life follow a normal distribution (e.g. height, mass, intelligence, etc.) When graphed as a histogram or frequency polygon, the normal distribution has a bell shape, and is often referred to as the Bell Curve. Frequency Normal Distribution Curve (The Bell Curve) Mark the mean, median, and mode on the normal curve above. How much of the data is below the mean? How much is above the mean? Properties of a Normal Distribution: The mean, median, and mode are ______________. The graph is symmetrical about the mean, i.e. _______ of the data is lower than the mean and _______ is larger than the mean. The total area under the curve represents ________% of the data. Almost all the data lie within _____ standard deviations of the mean (________________ __________________________). Math 20-2 Statistics: Lesson #4 The 68-95-99 Rule: About _________% of the population is within 1 standard deviation of the mean. About _________% of the population is within 2 standard deviations of the mean. About _________% of the population is within 3 standard deviations of the mean. 3 2 2 3 e.g. 1) Look at the data collected for the whole class’ rolls of two dice. Does this data approximate a normal distribution? Explain why or why not. Math 20-2 Statistics: Lesson #4 e.g. 2) A company has determined that the lifetime of the car battery it produces is normally distributed with a mean of 6 years and a standard deviation of 11 months. a) Sketch a graph of this distribution. Label the divisions on the horizontal axis. b) What percent of batteries will have a lifetime of 50 to 83 months? c) Out of a shipment of 450 batteries, how many would you expect will have a lifetime over 61 months? d) If the company wants to offer a warranty on its batteries. For how many months should the batteries be covered by the warranty if the manufacturer wants to replace no more than 2.5% of the batteries sold? Assignment: p. 279-282 #1, 6-7, 9-11, 16