STAT 210 1ST EditionGradeBuddyLecture 15Last LectureI. Describing Relationships for Categorical VariablesII. DistributionsIII. Simpson’s ParadoxThis LectureIV. Normal distributionsV. Properties of distributionsVI. How to solve distribution equationsCurrent LectureVII. 2 types of distributions are normal and student’s t distributionsVIII. This lecture is on normal distributionsIX. Normal curve is a symmetric bell shapeX. Normal distribution is an example of a continuous distributionXI. Notation X ~ N (, )XII. Propertiesa. Normal curve is bell shapedb. Peak of the curve is population mean c. Normal curve is symmetric about d. Center and spread are completely specified by specifying the values of the population mean and standard deviation e. Total area under normal curve is 1 or 100%f. 68-96-99.7% rulei. 68% fall within one standard deviationii. 95% fall within one standard deviationiii. 99.7% fall within one standard deviationXIII. Types of problemsXIV. Probabilitya. Find P(X = x), Find P( X < x) or P(X x), Find P(X > x), Find P(X > x), Find P (X x), Find P(x1 < X < x2) or Find P(x1 x x2)b. Special rule: P(X = x) = 0 for any XXV. Standard normal distribution a. Denoted by Zb. = 0c. = 1d. Shape is normal (symmetric bell curve)e. No unusual featuresf. Z ~ N(0,1)STAT 210 1ST EditionXVI. Normal Tablea. Gives the probability that the standard normal variable Z falls below somespecified valueb. Greater than problems can be solved by simply changing them to less than problemsi. P(Z > z) = 1 1-P(Z <z)c. Between problems are the samei. P(a < Z < b) = P(Z < b) – P(Z <
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