SOLUTION: A normal distribution with a mean of 55 and a standard deviation of 6 is evaluated to solve a business problem. What is the probability that any value in the population is between

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Question 133478: A normal distribution with a mean of 55 and a standard deviation of 6 is evaluated to solve a business problem. What is the probability that any value in the population is between 55 and 65? ___________. What is the probability that any value in the population is between 45 and 65? ____________.
Answer by stanbon(75887) (Show Source):
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A normal distribution with a mean of 55 and a standard deviation of 6 is evaluated to solve a business problem. What is the probability that any value in the population is between 55 and 65? ___________. What is the probability that any value in the population is between 45 and 65? ____________.
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You need the z-values of these various numbers.
Z(55) = 0 ; z(65) = (65-55)/6 = 5/6
P(55 < x < 65) = P(0 < z < 5/6) = 0.2977
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z(45) = (45-55)/6 = -10/6
P(45 < x < 65) = P(-10/6 < z < 5/6) = 0.74988...
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Cheers,
Stan H.