Bicycling Standards
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What percentage of chains purchased from this supplier fail to meet the manufacturer’s length requirement?
A manufacturer of racing bicycles installs a high performance derailleur gear system that requires a chain of length between 53.75” and 54.25 inches in order to work as properly. Suppose this manufacturer purchases chains from a long time supplier who makes bicycle chains by connecting individual chain links together. These chain links have a mean length of 0.5” and a standard deviation of 0.01.
you expect to have.. 108 chain links to form the desired chain…
but the error must be less than 0.25 from 54 inches…
0.25/108 = 0.0023
X – discrepancy of one individual chain link
P(-0.0023 < X < 0.0023) = 2 P( 0 < Z < 0.2315) = 0.182
these are the ones that will meet the requirement..
81.8% will fail to meet the requirement.
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