Chapter 7 (Sp12)

# Chapter 7 (Sp12) - Section 7.1 Properties of the Normal...

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Section 7.1 – Properties of the Normal Distribution Probability Density Function – An equation used to compute probabilities of continuous random variables. It must satisfy the following 2 properties: 1. Every point on the curve has a vertical height greater than 0. 2. Total area under the curve must equal 1 ***The area under the curve = Probability*** Normal Distribution – A continuous random variable is normally distributed if it is symmetric and bell-shaped. Properties of the Normal Density Curve: 1. Symmetric about the mean, μ. 2. Mean = Median = Mode, so there is a single peak and the highest point occurs at x = μ. 3. Inflection points occur at μ σ and μ + σ. 4. The area under the curve = 1. 5. The areas to the right and left of μ are both equal to ½. 6. As x increases and decreases without bound, the graph approaches (but never touches) the horizontal axis. 7. The Empirical Rule applies: Approximately 68% of the area under the curve is between μ σ and μ + σ Approximately 95% of the area under the curve is between μ – 2 σ and μ + 2 σ Approximately 99.7% of the area under the curve is between μ – 3 σ and μ + 3 σ (see pg. 376) 1

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The normal curve is a mathematical model (an equation, table, or graph that is used to describe reality). The normal curve does a good job of describing the distribution of things like height, IQ scores, birth weights, etc. Example : The heights of 10-year-old males are normally distributed with a mean of 55.9 inches and a standard deviation of 5.7 inches. a) Draw a normal curve with the parameters labeled. b) Shade the region that represents the proportion of 10-year-old males who are less than 50.2 inches tall. c)
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## This note was uploaded on 01/06/2012 for the course MATH 1342 taught by Professor Lisajuliano during the Spring '12 term at Collins.

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Chapter 7 (Sp12) - Section 7.1 Properties of the Normal...

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