SOLUTION: A business school claims that the average income of graduates of this school three years after graduation is $700. a. If the claim is correct and if incomes are normally distribut

Question 363826: A business school claims that the average income of graduates of this school three years after graduation is $700.
a. If the claim is correct and if incomes are normally distributed with a standard deviation of $60, what is the probability that 36 randomly selected graduates have an average income of less than $675?
b. If a random sample of 36 graduates had an average weekly income of $675, what would you conclude about the validity of the claim?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A business school claims that the average income of graduates of this school three years after graduation is $700.
a. If the claim is correct and if incomes are normally distributed with a standard deviation of $60, what is the probability that 36 randomly selected graduates have an average income of less than $675?
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t(675) = (675-700)/[60/sqrt(36)] = -2.5
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P(x-bar < 675) = P(t < -2.5 when df=36) = tcdf(-100,-2.5,35) = 0.0086
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b. If a random sample of 36 graduates had an average weekly income of $675, what would you conclude about the validity of the claim?
Pretty rare occurrence.
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Cheers,
Stan H.

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