Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is normal with mean $360 and standard deviation $50. What is the P(X>$400)?
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P( X >400 )= P (X- 360> 40) = P((X - 360)/50 > 40/50)
ie P(Z >.8) = 1 - P(Z <.8) = 1 - .7881 = .2119 (Using tables of the Normal probability function.
ie P(Z >.8) = 1 - P(Z <.8) = 1 - .7881 = .2119 (Using tables of the Normal probability function.
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z = (400 - 360) / 50 = 0.6666
Then find look up z on the z-table, which gives 0.4949 = 49.49% is for P(X<$400), since by definition a z-score gives the probability of it BELOW that point, so for greater than $400 we need P(X>$400) = 100% - 49.49% = 50.51%
Then find look up z on the z-table, which gives 0.4949 = 49.49% is for P(X<$400), since by definition a z-score gives the probability of it BELOW that point, so for greater than $400 we need P(X>$400) = 100% - 49.49% = 50.51%