A sample of the monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical Rule, about 95 percent of the monthly food expenditures are between what two amounts?
A) $100 and $200
B) $85 and $105
C) $205 and $220
D) $110 and $190

Question

Quizplus · Accepted Answer

The Empirical Rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean. 
In this case, since the sample approximates a symmetrical distribution, we can use the Empirical Rule to estimate that about 95% of the monthly food expenditures are between one standard deviation below and one standard deviation above the mean. 
One standard deviation below the mean is $150 - $20 = $130, and one standard deviation above the mean is $150 + $20 = $170.
Therefore, about 95% of the monthly food expenditures are between $130 and $170, and the best choice is D, which includes this range.

A Sample of the Monthly Amounts Spent for Food by Families