Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 3 - Data Description - 3-2 Measures of Variation - Exercises 3-2 - Page 146: 40



Work Step by Step

Empirical rule: • Approximately 68% of the data values will fall within 1 standard deviation of the mean. • Approximately 95% of the data values will fall within 2 standard deviations of the mean. • Approximately 99.7% of the data values will fall within 3 standard deviations of the mean. 40. Citrus Fruit Consumption The average U.S. yearly per capita consumption of citrus fruit is 26.8 pounds. Suppose that the distribution of fruit amounts consumed is bell-shaped with a standard deviation equal to 4.2 pounds. What percentage of Americans would you expect to consume more than 31 pounds of citrus fruit per year? We can use the empirical rule for this bell-shaped distribution. 31 corresponds to $\frac{31-26.8}{4.2}=1$ standard deviation away and we know there are $68%$ within $22.6-31$ and there will be $1-0.68=0.32$ outside and the region, so 31and above would be half or $0.16$ which is the answer.
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