9 The monthly amounts spent for food by families of four rec

9. The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $ 150 and the standard deviation as $20. Using the Empirical Rule, about 95% of the month4y food expenditures are between what two amounts? A $ 100 and $200 B. $85 and $105 C. $205 and $220 D. $110 and $190

Solution

The empirical rule states that 68% of the data will fall with 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 standard deviations of the mean.

Step 1: We want to know which food expenditures are 95% of the data. This would correspond to 2 standard deviations each way from the mean.

Step 2: The mean is $150 and the standard deviation is $20. Adding 2 standard deviations and subtracting 2 standard deviations:

=$150+2*($20)=$190

$150-2*($20)=$110

Solution:

95% of monthly expenditures are between $110 and $190. Answer D.

Hope this helps! :) Let me know if you have any other questions.