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

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 7.5 grams of fat per pound. A random sample of 40 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 40 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Explanation / Answer

Given data:

Population Mean, M = 32

Population SD, S = 7.5

Sample size, n = 40

Sample mean, X = 29.7

Calculating the test statistic:

z = (X-M)/(S/n0.5) = (29.7-32)/(7.5/400.5) = -1.9395

The corresponding p-value for this z-score is:

p = 0.02622

Hope this helps !

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