EXAMPLE 1.33 Standardizing Potato Chip Bag Weights

The weights of 9-ounce potato chip bags are approximately Normal with ounces and ounce. The standardized weight is

A bag’s standardized weight is the number of standard deviations by which its weight differs from the mean weight of all bags. A bag weighing 9.3 ounces, for example, has standardized weight

or 1.2 standard deviations above the mean. Similarly, a bag weighing 8.7 ounces has standardized weight

or 2.8 standard deviations below the mean bag weight.