39 Armstrong Faber produces a standard number two pencil called Ultra-Lite. Since Chuck Armstrong started Armstrong Faber, sales had grown steadily.

With the increase in the price of wood products, however, Chuck has been forced to increase the price of the Ultra-Lite pencils. As a result, the demand for Ultra-Lite has been fairly stable over the past six years. On the average, Armstrong Faber has sold 457,000 pencils each year. Furthermore, 90%
of the time sales have been between 454,000 and 460,000 pencils. It is expected that the sales follow a normal distribution with a mean of 457,000 pencils.
Estimate the standard deviation of this distribution.
( Hint: Work backward from the normal table to find Z . Then apply Equation 12.)