SOLUTION: For a normal population with population = 70 and population standard deviation = 20, what is the probability of obtaiing a sample mean equal to or greater than 75 for a random samp

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Question 614691: For a normal population with population = 70 and population standard deviation = 20, what is the probability of obtaiing a sample mean equal to or greater than 75 for a random sample of n= 225? How do you arrive at the probability by reporting the standard error and the z-score?
Answer by stanbon(75887) About Me  (Show Source):
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For a normal population with population with u = 70 and population standard deviation = 20, what is the probability of obtaining a sample mean equal to or greater than 75 for a random sample of n= 225? How do you arrive at the probability by reporting the standard error and the z-score?
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mean of the sample means = 70
std of the sample means = 20/sqrt(225) = 20/15 = 4/3
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z(75) = (75-70)/15 = 5/15 = 1/3
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P(x-bar > 75) = P(z > 1/3) = normalcdf(1/3,100) = 0.3694
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Cheers,
Stan H.
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