Menhaden are an abundant, but inedible, ocean fish of the Atlantic and Gulf wate

Question

Menhaden are an abundant, but inedible, ocean fish of the Atlantic and Gulf waters that are harvested commercially as a nutritional source of omega-3 fatty acid. They are ground up for fish meal and fertilizer and also serve as a major food source for sea bass and other more commercial fish. The lengths of menhaden are approximately normally distributed with a mean length of 12 inches and a standard deviation of 2.5 inches. If you were to commercially catch 20,000 menhaden, which one of the following intervals would you expect to contain approximately 8000 menhaden? (A) (B) (C) 0 to 11.87 inches 8.80 to 12.5 inches 8.80 to 15.20 inches 10.69 to 13.31 inches 10.69 to 14.10 inches (D) (E) 41

Explanation / Answer

for 8000 is equaivalent to 8000/20000 =0.4 middle proportion for which lies between 30th and 70 th percentile

for 30th and 70 th percentile ; z score =0.5244

therefore corresponding value =mean -/+ z*std deviaiton =10.69 to 13.31

option D is correct

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