Week5_Part_A

# Week5_Part_A - Week 5: Normal Distributions Graphs of...

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Click to edit Master subtitle style Larson/Farber Ch 5 Week 5: Normal Distributions l Graphs of Normal Distributions l Standard Units and Areas Under the Normal Curve l Areas Under the Normal Curve

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Larson/Farber Ch 5 22 l Numerical outcome of an experiment Weight of a student l Observe 115, 156.8, 190.1, 225 l Continuous random variable Whole or fractional number Obtained by measuring Infinite number of values in interval Continuous Random Variable
Larson/Farber Ch 5 33 The Normal Distribution l The normal distribution is a continuous distribution that applies to an enormous variety of naturally occurring variables l Many other variables tend to assume normal probability distributions under certain conditions μ

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Properties of a Normal Distribution x Inflection point Inflection point The total area under the curve is one or 100%The curve approaches but never touches the x- axis as it extends farther away from the mean. The graph curves downward between μ - σ and μ + σ and curves upward to The points at which the curvature μ - σ μ + σ
Larson/Farber Ch 5 55 Normal Distributions: Means and Standard Deviations Curves with different means, same standard deviation 2 1 1 1 1 1 1 1 1 1 1 2 2 9 1 2 1 5 1 8 1 0 1 1 1 3 1 4 1 6 1 7 1 9 2 0 Curves with different means different standard deviations

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Larson/Farber Ch 5 66 Empirical Rule About 95% of the area lies within 2 standard deviations About 99.7% of the area lies within 3 standard deviations of the mean +2σ -2σ +1σ +3σ -1σ -3σ μ 68% About 68% of the area lies within 1 standard deviation of the mean
Larson/Farber Ch 5 77 Determining Intervals An instruction manual claims that the assembly time for a product is normally distributed with a mean of 4.2 hours and standard deviation 0.3 hours.

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## This note was uploaded on 05/17/2011 for the course BIS 115 taught by Professor Wright during the Spring '10 term at DeVry Chicago.

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Week5_Part_A - Week 5: Normal Distributions Graphs of...

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