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 40 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 40 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Answer 1

The probability of observing a sample mean of 31.5 grams of fat per pound or less in a random sample of 40 farm-raised trout is 0.473.

Step-by-step explanation:

To find the probability of observing a sample mean of 31.5 grams of fat per pound or less in a random sample of 40 farm-raised trout, we can use the Z-score formula and the standard normal distribution.

First, calculate the Z-score: Z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

Z = (31.5 - 32) / (7 / sqrt(40)) = -0.0717

Next, look up the Z-score in the standard normal distribution table to find the corresponding probability. In this case, the probability is 0.4726.

Rounding the answer to three decimal places, the probability of observing a sample mean of 31.5 grams of fat per pound or less in a random sample of 40 farm-raised trout is 0.473.