Question

Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of

32 grams of fat per pound, with a standard deviation of 7 grams of fat per pound. A random sample of 35  farm-raised trout is selected. The mean fat content for the sample is 31.5 grams per pound. Find the probability of observing a sample mean of 31.5 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.

Answer 1

Here, μ = 32, σ = 7/sqrt(35) = 1.1832 and x = 31.5.

We need to compute P(X <= 31.5). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (31.5 - 32)/1.1832 = -0.4226

Therefore,
P(X <= 31.5) = P(z <= (31.5 - 32)/1.1832)
= P(z <= -0.4226)
= 0.336

Ans: = 0.336