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Notes: Hmwk Precalculus – Chapter 13: Statistics and Probability Section 13-5: Normal Distributions (Page 889) Normal Curve – bell curve Normal distributions – used to predict the outcomes of many events o Used to predict if an outcome is statistically significant or just by chance o Symmetric about the mean o X-axis is a horizontal asymptote o Area under the curve is 1 o The maximum is at the mean o Has two points of inflection (at 1 standard deviation to the right and to the left of the mean) o Mean, median, and mode are all the same value (the center), μ Standard Normal Curve – mean of 0 and a standard deviation of 1 o Parent function for all normal curves o Change in μ horizontal translation o Change in σ horizontal stretch and vertical compression or vice versa –(x- μ)2 Equation of a Normal Curve: y = 1 e 2σ2 σ √(2π) Empirical Rule: o 68% within 1 σ o 95% within 2 σ o 99.7% within 3 σ Standardize – make it match a standard normal distribution Z-value – number of standard deviations that a data value is above the mean o Z = (x – μ) / σ where x is the data point, μ is the mean, and σ is the standard deviation o Area under a normal curve between x = a and x = b is equal to the are under the standard normal curve between the z-value of a and the z-value of b Page 896: 1 – 29 odd