Suppose you are told that a company has produced widgets that have a normally distributed weight with a 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.

Write a response to the following questions:

• If they consider a widget defective when it is three 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 usually distributed?
• If the weights of the widgets were skewed left, how would that impact your previous responses?
• When you determined your z-score based on the random number, what did that number mean? What would the company do with the widget-bawidget basedlucky number?