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 34 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 grams of fat per pound or less in a random sample of 34 farm-raised trout.

The probability of observing a sample mean of 31.1 grams of fat per pound or less in a random sample of 34 farm-raised trout is 0.227

Step-by-step explanation:

Let X be the sample mean of fat in 34 farm-raised trout

The probability of observing a sample mean of 31.1 grams of fat per pound or less in a random sample of 34 farm-raised trout can be stated as:

P(X<31.1 grams) = P(z<z*)

where z* is the z-statistic of sample mean of 31.1 grams fat.

z* can be calculated as follows:

z*= where

Then z*= ≈ −0.7497

and P(z<z*) ≈ 0.227

The probability of observing a sample mean of 31.1 grams of fat per pound or less in a random sample of 34 farm-raised trout is 0.227

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step-by-step explanation: