Question

the weights of a particular size of boxes of apple cinnamon cheerios are approximately normally distributed with mean weight 23.3 oz and standard deviation 0.2 oz. they wish to reject any box of cereal that weighs less than the listen weight of 22.7 oz. based on the empirical rule (68/95/99.7), what percentage of cereal boxes will General Mills reject?

Answer 1

0.15%, or 15/100 of 1%, or 3/20 of 1%

Explanation:

68% of the data lies within 1 standard deviation of the mean (23.3 oz), or between 23.1 oz and 23.5 oz.

95% of the data lies within 2 std. dev. of the mean, or between 22.9 oz and 23.3 oz.

99.7% of the data lies within 3 std. dev of the mean, or between 22.7 oz. and 23.1 oz.

The remaining area under the curve is 100% - 99.7%, or 0.3%, Only half of this, or 0.15%, is to the left of 22.7 oz.