Question

Hockey pucks used in professional hockey games must weigh between 5.5 and 6 ounces. if the weight of pucks manufactured by a particular process is bell-shaped and has mean 5.75 ounces, how large can the standard deviation be if 99.7% of the pucks are to be usable in professional games?

Answer 1

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
`5.5=5.75-3* SD`

`3* SD=5.75-5.5`

`SD=(0.25)/(3) =0.083`

Also
`6=5.75+3* SD`

`3* SD=6-5.75`

`SD=(0.25)/(3) =0.083`

So if 99.7% of the pucks are to be usable in professional games, the standarddeviation should be 0.083.