(Solved): Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an ave ...

Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average (mean) of 32 grams of fat per pound, with a standard deviation of \( 8 \mathrm{grams} \) of fat per pound. A random sample of 35 farm-raised trout is selected. The mean fat content for the sample is \( 31.1 \) grams per pound. Find the probability of observing a sample mean of \( 31.1 \mathrm{grams} \) of fat per pound or less in a random sample of 35 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.