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Answer :
Final answer:
The problem is a common statistics problem involving the calculation of probabilities within a certain range in a normally distributed set of scores. We must first calculate the Z-scores for the given values, then find the corresponding probabilities, and take the difference of these probabilities to find our answer.
Explanation:
The subject of the question is related to the field of statistics, as it is about calculating probabilities based on standard deviation and sample averages. The general process of calculating a Z-score is needed: Z = (X - μ) / σ, where X is the value in the dataset, μ is the mean, and σ is the standard deviation.
Here, you have a distributed group of scores represented by the average annual consumption of canned fruit among Americans. With 39 pounds as the mean and a standard deviation of 3.2 pounds. Because we're looking at a sample of 47 individuals, we use the standard deviation of the sample mean to get the Z scores. In this case, the standard deviation of the sample mean is the standard deviation of the population divided by the square root of the sample size (~3.2/√47).
You are then able to calculate the Z-scores for 38.2 and 39.4 pounds, and use these scores to find the corresponding probabilities for each. The probability within this range will be the difference between these two probabilities.
Learn more about Z-score here:
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