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16.1 Approximate Normal Approximately Normal Distribution: Almost a bell shape curve. Normal Distribution: Bell shape curve. All perfect bell shape curves are normal curves. Discrete Math

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16.2 Normal Distribution: center = median (M) = mean ( ) Approx Normal: Median Mean. Point of inflection: transition point of being bent upward to downward. Normal Distribution: The standard Deviation equals the distance between a point of inflection and the axis of symmetry. Discrete Math To be continued…

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16.2 (Continued...) Q 1 - (0.675) Q 3 + (0.675) Discrete Math

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16.3 Standardizing Normal Data Measuring data values using the standard deviation. Standardizing Original Data x Standardized Data z = (x- ) / (z-value) Discrete Math

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16.4 68 - 95 - 99.7 Rule 68% of data within one standard deviation from the mean. 95% of data within two standard deviations from the mean. 99.7% of data within three standard deviations from the mean. Range 6 Discrete Math

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16.5 - 7 Honest coin principal: A coin is tossed n times and X is the number of heads. The random variable X has an approximately normal distribution with mean = n / 2 and standard deviation = n / 2 256 tosses: = 256 / 2 = 128, = 256 / 2 = 8 Discrete Math To be continued…

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16.5 - 7 (Continued...) Dishonest coin principal: A dishonest coin is tossed n times and X is the number of heads. Suppose p is the probability of heads and (1-p) is the probability of tails. The random variable of X has an approximately normal distribution with mean = n * p and standard deviation = ( n * p * (1 - p)) 1000 light bulbs, 20% defects: = 1000(.20) = 200 = 1000 * (.20) * (1 -.20) Discrete Math To be continued…

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16.5 - 7 (Continued...) Standard Error: The standard deviation of the sampling distribution expressed as a percentage. / N Confidence Intervals: 95% two standard deviations from the mean. 99.7 three standard deviations from the mean. Discrete Math

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