Analytics Exercise $13-4($Static$)$

Quality Control Analytics at Toyota

As part of the process for improving the quality of their cars, Toyota engineers have identified a potential improvement to the process that makes a washer that is used in the accelerator assembly. The tolerances on the thickness of the washer are fairly large since the fit can be loose, but if it does happen to get too large, it can cause the accelerator to bind and create a potential problem for the driver. $($Note: This case has been fabricated for teaching purposes, and none of these data were obtained from Toyota.$)$

Let$$s assume that, as a first step to improving the process, a sample of $40$ washers coming from the machine that produces the washers was taken and the thickness measured in millimeters. The following table has the measurements from the sample:

$1\mathrm{.}92\mathrm{.}01\mathrm{.}91\mathrm{.}82\mathrm{.}21\mathrm{.}72\mathrm{.}01\mathrm{.}91\mathrm{.}71\mathrm{.}81\mathrm{.}82\mathrm{.}22\mathrm{.}12\mathrm{.}21\mathrm{.}91\mathrm{.}82\mathrm{.}11\mathrm{.}61\mathrm{.}81\mathrm{.}62\mathrm{.}12\mathrm{.}42\mathrm{.}22\mathrm{.}12\mathrm{.}12\mathrm{.}01\mathrm{.}81\mathrm{.}71\mathrm{.}91\mathrm{.}92\mathrm{.}12\mathrm{.}02\mathrm{.}41\mathrm{.}72\mathrm{.}22\mathrm{.}01\mathrm{.}62\mathrm{.}02\mathrm{.}12\mathrm{.}2$

If the specification is such that no washer should be greater than $2\mathrm{.}4$ millimeters, assuming that the$$thicknesses are distributed normally, what fraction of the output is expected to be greater than this thickness?

Note: Round your percentage answer to $4$ decimal places.