Question 1026698: The heights of men in the Canada are normally distributed with a mean of 68 inches and a standard deviation of 4 inches.
a) What is the probability that a randomly selected man is taller than 70 inches?
b) A random sample of five men is selected. What is the probability that the sample mean is greater than 70 inches?
c) What is the probability that the mean height of a random sample of 36 men is greater than 70 inches?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The heights of men in the Canada are normally distributed with a mean of 68 inches and a standard deviation of 4 inches.
a) What is the probability that a randomly selected man is taller than 70 inches?
z(70) = (70-68)/4 = 1/2
P(x < 70) = P(z > 1/2) = normalcdf(1/2,100) = 0.3085
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b) A random sample of five men is selected. What is the probability that the sample mean is greater than 70 inches?
t(70) = (70-68)/[4/sqrt(5)] = 2sqrt(5)/4 = 1.1180
P(x-bar > 70) = P(t > 1.1180 when df = 4) = tcdf(1.1180,100,4) = 0.1631
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c) What is the probability that the mean height of a random sample of 36 men is greater than 70 inches?
z(70) = (70-68)/4/(sqrt(36)) = 2*6/4 = 3
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P(x-bar > 70) = P(z > 3) = normalcdf(3,100) = 0.0013
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Cheers,
Stan H.
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