Question

The average us yearly per capita consumption of citrus fruit is 26.8 pounds. suppose that the fruit amounts consumed is bell shaped with a standard deviation of 4.2 pounds. using empirical normal rule find the percentage of americans you would expect to consume more than 31 and 35.2 pounds of citrus per year?

Answer 1

Using the empirical normal rule, approximately 16% of Americans are expected to consume more than 31 pounds of citrus fruit per year, and approximately 2.5% are expected to consume more than 35.2 pounds per year.

Step-by-step explanation:

The question involves the application of the empirical rule (or the 68-95-99.7 rule) of normal distribution to determine what percentage of Americans consume more than specific amounts of citrus fruit per year. According to the empirical rule for a normal distribution, approximately 68% of data is within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. The average us yearly per capita consumption of citrus fruit is 26.8 pounds with a standard deviation of 4.2 pounds.

To find the percentage of Americans consuming more than 31 pounds, we calculate the z-score: (31 - 26.8) / 4.2 = 1. This indicates that 31 pounds is one standard deviation above the mean. Referring to the empirical rule, about 16% (50% of the second half minus approximately 34% within one standard deviation) would be expected to consume more than 31 pounds.

For 35.2 pounds, the z-score is (35.2 - 26.8) / 4.2 = 2, which is two standard deviations above the mean. Thus, using the empirical rule, approximately 2.5% (50% minus 47.5%, which represents the proportion within two standard deviations above the mean) of Americans are expected to consume more than 35.2 pounds of citrus per year.