A plastic cap should fit a metal container, as shown in the figure. The external

Question

A plastic cap should fit a metal container, as shown in the figure. The external diameter of the metal container shows normal behavior with an average of 3 "and standard deviation of 0.005". The internal diameter of the plastic lid is also normally distributed with an average of 2.999 and a standard deviation of 0.006 ". Previous studies have determined that a spill will occur when the diameter of the lid is greater than the outside of the container by more than 0.003 ". On the other hand, if the external diameter of the container is greater than the internal diameter of the lid by more than 0.01 inches, the lid can not be adjusted to the container.

Determine the% of products in which the spill will occur.

Determine the% of products that can not be assembled (lid does not enter the container.

Explanation / Answer

here let external diameter is X and diameter of lid is Y,

their mean difference =3-2.999=0.001

there combined std deviation is (0.0052+0.0062)1/2 =0.00781

for normal distribution z score =(X-mean)/std deviaiton

a) hence probability of products in which the spill will occur =P(Y-X>0.003)=P(Z>(0.003-(-0.001))/0.00781)

=P(Z>0.5121) =0.3043 ~30.43%

b) % of products that can not be assembled =P(X-Y>0.01)=P(Z>(0.01-0.001)/0.00781)

=P(Z>1.1523)=0.1246 ~ 12.46%

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