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Discrete Math 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 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. To be continued… Discrete Math 16.2 (Continued...) • Q1 - (0.675) • Q3 + (0.675) Discrete Math 16.3 Standardizing Normal Data Measuring data values using the standard deviation. • Standardizing • Original Data x (z-value) Standardized Data z = (x-) / Discrete Math 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 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 To be continued… Discrete Math 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) To be continued… Discrete Math 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