Suppose you are told that a company has produced widgets that have a normally distributed weight with mean of 74.5 ounces and a standard deviation of 3.1 ounces.

Choose a number randomly from 60 to 90 and determine the corresponding z-score.

• If they consider a widget defective when it is 3 or more standard deviations from the mean, what would be the lowest and highest weight still accepted?
• How do you think the company knew the weights of their widgets were normally distributed?
• If the weights of the widgets were actually skewed left, how would that impact your previous responses?
• When you determined your z-score based on the random number, what did that number actually mean? What would the company do with the widget based on your random number?