What should the mean diameter, in inches, be in order to minimize the fraction of bearings that are scrapped?

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answer :  3.000 inches

Step-by-step explanation:

In order to minimize the fraction of bearings that are to be scrapped The mean diameter in inches should be 3.000 inches and this is because the diameter of the bearings follows a normal distribution.

The higher the fraction of accepted bearings, the minimal the fraction of rejected fraction bearings

specifications of bearing diameter; 3.000 ± 0.002

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)