Question

The weight of dog food in a local grocery store is normally distributed. The mean weight is 90 pounds with a standard deviation of 3.5 pounds. How much do the middle 99.7% of the dog food weigh?

Between 83 and 97 pounds
Between 79.5 and 100.5 pounds
Between 86.5 and 93.5 pounds
Between 70 and 90 pounds

Answer 1

Note that "middle 99.7%" signifies "within 3 standard deviations of the mean."

Thus, add 3 standard deviations to the mean (90 lb) to get the high end weight and subtract 3 std devs to get the low end weight:

90 lb + 3(3.5 lb) = 100.5 lb

90 lb - 3(3.5 lb) = 79.5 lb

So the middle