In: Statistics and Probability
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Answers for Z-values should be 2 decimals, probabilities should be 3 decimals, X-values 1 decimal. If σX = the standard deviation (SD) of X and µX = the mean of X, then:
Z Formula 1: X to Z → Z0 = (X0 - µX) / σX
Z Formula 2: Z to X → X0 = µX + (Z0 * σX)
Given μX = 8.3, σX = 3.2
a) Find X0 such that prob(X0 < X < 10) = .38
b) Find X1 such that prob(5.1 < X < X1) = .59
c) Find the 78.81st percentile of X