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Answer :
The question is portraying a scenario in statistics where the consumption of red meat is normally distributed with a known mean and standard deviation.
Sampling from this distribution, the standard error and mean can be found by simple calculations. The graph of the sampling distribution would also follow a normal curve centered around the sample mean.
The subject matter of this question is statistics, specifically dealing with the concept of the sampling distribution of a mean, standard error, and normal distribution.
In the context of the question, it's said that the consumption of red meat is normally distributed with a mean of 118 pounds and a standard deviation of 38.7 pounds. When a sample is taken from this population of size 17, the mean consumption and standard error of the mean can be calculated.
The formula to find the standard error of the mean is the population standard deviation divided by the square root of the sample size. In this case, the standard error would be 38.7/√17 ≈ 9.39 pounds.
For the motion of the mean, it doesn't change when taking a sample from the whole population, hence it remains 118 pounds. The graph of the sampling distribution would resemble a normal distribution curve centered around the mean of 118 lbs with a standard error of 9.39 pounds. The width of the graph would be based on the sizes of these errors.
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