Question 629237: In a particular region of Cape Cod, it is known that lobstermen trap on average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?
Place your answer, rounded to four decimal places, in the blank. When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a particular region of Cape Cod, it is known that lobstermen trap on average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?
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z(31.5) = (31.5-32)/[4/sqrt(30)] = -0.6847
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P(x-bar < 31.5) = P(z < -0.6847) = normalcdf(-100,-0.6847) = 0.2468
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Note: If you use a t-distribution you will get a slightly different
answer.
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Cheers,
Stan H.
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