Question 467292: A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 2 inches. A random sample of 36 fish is taken from the tank. Let x-bar be the mean sample length of these fish. What is the probability that x-bar is within 0.5 inch of the claimed population mean?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 2 inches. A random sample of 36 fish is taken from the tank. Let x-bar be the mean sample length of these fish. What is the probability that x-bar is within 0.5 inch of the claimed population mean?
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t(15.5) = (15.5-15)/[2/sqrt(36) = 1.5
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t(14.5) = (14.4-15)/[2/sqrt(36)] = -1.5
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P(14.5 < x-bar < 14.5) = P(-1.5 < t < 1.5)
= tcdf(-1.5,1.5,36) = 0.8574
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Cheers,
Stan H.
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