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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?

Round your answer to four decimal places. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry.

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