The Normal Probability Density Function



Chapter 24A | p 631The Normal DistributionFor a continuous variable, we only talk about the probability that an event lies in an INTERVALThe probability that X is EXACTLY a value is ZERO (because it is measured)Therefore…Pc≤X≤d=Pc<X<dright24902800left24193500The Normal Probability Density Functionright147582400FeaturesThe normal curve is SYMMETRICAL about the line x=μAs x approaches ±∞, the normal curve approaches its asymptote, the x-axisF(x) > 0 for all xArea under the curve = 1right222453Bell shapeChapter 24C | p. 639The Standard Normal Distribution (Z-Distribution)253280727783200Every normal X-distribution can be transformed into the standard normal distribution or Z-distribution using the transformation:z=x-μσZ-score represents the number of standard deviations a point is from the meanChapter 24D | p. 644Quantiles or k-valuesPX≤K=0.95Quantile – the k-value in the above equationUse the INVERSE NORMAL Cumulative function on the calculator In some questions, we must convert to z-score to find unknown mean or standard deviation ................
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