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 8 grams of fat per pound. A random sample of 34 farm-raised trout is selected. The mean fat content for the sample is 29.7 grams per pound. Find the probability of observing a sample mean of 29.7 grams of fat per pound or less in a random sample of 34 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

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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 8 grams of fat per pound. A random sample of 34 farm-raised trout is selected. The mean fat content for the sample is 29.7 grams per pound. Find the
probability of observing a sample mean of 29.7 grams of fat per pound or less in a random sample of 34 farm-raised trout.
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Transcribed Image Text: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 8 grams of fat per pound. A random sample of 34 farm-raised trout is selected. The mean fat content for the sample is 29.7 grams per pound. Find the probability of observing a sample mean of 29.7 grams of fat per pound or less in a random sample of 34 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Expert Solution
Step 1

Farm-raised trout contain an average of 32 grams of fat per pound with a standard deviation of 8 grams of fat per pound.

So, mean, µ = 32 

and, standard deviation, σ = 8

34 random samples are collected. 

Let, X be the sample mean of 34 random samples. 

Here, number of samples , n = 34

By central limit theorem,

Z = n(X-µ)σ=34(X-32)8 ~N(0,1)

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