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 Thread: Probability/Stats Questions? View Single Post
 07-28-2007 #3 Hobart Guest   Posts: n/a a) To find the probability of a variable, X, between two limits, a and b when the variable is normally distributed:P(a < X < b) = Î¦[(b-Âµ)/Ïƒ] - Î¦[(a-Âµ)/Ïƒ] where the values within the square brackets are standard normal z-values. Phi (Î¦) is and operator that means "find the probability associated with the Z-values in the square brackets". So evaluating:P(550 < X < 650) = Î¦[(650-550)/80] - Î¦[(550-550)/80] P(550 < X < 650) = Î¦[(650-550)/80] = Î¦[1.25] - Î¦[0] = 0.8944 - 0.50 = 0.3944b) You want to eliminate the bottom 20%. So the Z-value associated with the BOTTOM 20% is -0.84, and the limit for the bottom 20% is found by:-0.84 = (x - 550)/80; solving for x = 482.8. If an integer is required, then the lowest acceptable score would be 483.c) Find the probability that the sample mean is less than 650:Z = (650-550)/(80/âˆš50) = 100/35.78) = 2.79Then Î¦[2.79] - Î¦[0] = 0.9974 -0.50 = 0.4974