Question 1026702: Suppose that the average annual revenue of a small business is $150 000 with a standard deviation of $40 000. Assume that the revenue distribution is normal.
a) What is the probability that one business selected at random makes less than $120 000?
b) What is the probability that the average annual revenue of a random sample of 4 businesses is less than $120 000?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose that the average annual revenue of a small business is $150 000 with a standard deviation of $40 000. Assume that the revenue distribution is normal.
a) What is the probability that one business selected at random makes less than $120 000?
z(120,000) = (120,000-150,000)/40000 = -3/4
P(x < $120,000) = P(z < -3/4) = normalcdf(-100,-3/4) = 0.2266
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b) What is the probability that the average annual revenue of a random sample of 4 businesses is less than $120 000?
t(120,000) = (120,000-150,000)/[40,000/sqrt(4)) = -30,000/20,000 = -3/2
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P(x-bar < 120,000) = P(t < -3/2 when df = 3) = tcdf(-100,-3/2,3) = 0.1153
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Cheers,
Stan H.
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