Solution: The weight of pucks manufactured by a particular process is bell-shaped and has mean 5.75 ounces
Therefore, we can use the Empirical Rule to find the standard deviation. Empirical Rule states that approximately 99.7% of all observations fall within three standard deviations of the mean.
Also we know that the acceptable range is between 5.5 and 6
So [tex]5.5=5.75-3\times SD[/tex]
[tex]3\times SD=5.75-5.5[/tex]
[tex]SD=\frac{0.25}{3} =0.083[/tex]
Also [tex]6=5.75+3\times SD[/tex]
[tex]3\times SD=6-5.75[/tex]
[tex]SD=\frac{0.25}{3} =0.083[/tex]
So if 99.7% of the pucks are to be usable in professional games, the standarddeviation should be 0.083.
