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Chapter 4: Problem 42

The article "Taxable Wealth and Alcoholic Beverage Consumption in the United States" (Psychological Reports [1994]: \(813-814\) ) reported that the mean annual adult consumption of wine was \(3.15\) gallons and that the standard deviation was \(6.09\) gallons. Would you use the Empirical Rule to approximate the proportion of adults who consume more than \(9.24\) gallons (i.e., the proportion of adults whose consumption value exceeds the mean by more than 1 standard deviation)? Explain your reasoning.

Short Answer

Expert verified
Without knowledge on whether the wine consumption data are normally distributed, applying the Empirical Rule is not recommended. Instead, data distribution should first be analyzed.

Step by step solution

01

Understand the Empirical Rule

The Empirical Rule, also known as the 68-95-99.7 Rule, states that for a normal distribution, approximately 68% of data falls within one standard deviation from the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. It's important to know that this rule applies specifically to normally distributed data.
02

Evaluate the Distribution

In the exercise, it is not explicitly mentioned that the wine consumption is normally distributed. Without this confirmation, the application of the Empirical Rule could lead to inaccurate results. If the data follow a skewed distribution (which is often the case in consumption data where a few individuals may consume significantly more than the average), the Empirical Rule would not be applicable as the proportions of observations around the mean would differ from those predicted by the rule.
03

Decision

As the distribution of wine consumption among all adults hasn't been mentioned as normally distributed, it would not be necessarily correct to use the Empirical Rule as basis for approximation in this particular case. An examination of data distribution would be required to confirm the suitability of using the Empirical Rule.

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Most popular questions from this chapter

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