Amstrong Faber produces a standard number two pencil called Ultra-Lite. Since Ch

Question

Amstrong Faber produces a standard number two pencil called Ultra-Lite. Since Chuck Amstrong started Amstrong Faber, sales have 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, Amstrong 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 the equation).

Explanation / Answer

90% of qualities are somewhere around 454000 and 460000, which are symmetric about the mean of 457000.

Consequently for the center 90%, the range of each external tail is (1-0.90)/2 = 0.05. Henceforth, the z score for that is, by table,

z = 1.645

Consequently, for x = 460000

sigma = (x-u)/z = (460000-457000)/1.645 = 1823.71 [ANSWER]

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