Answer
$16\%$
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.
