The lengths of a certain component are normally distributed with a mean of 250 m

Question

The lengths of a certain component are normally distributed with a mean of 250 mm and a standard deviation of 0.6 mm. Four of the components are joined end-to-end and fitted into a slot.

a. If the slots have length 1002.5 mm, what proportion of the time will four randomly selected components be able to fit into the slot?

b. Suppose that the lengths of the slots are normally distributed with a mean of 1002.5 mm and a standard deviation of 0.4 mm. What proportion of the time will four randomly selected components be able to fit into the slot?

Explanation / Answer

a) mean lkength of 4 components =250*4=1000

and std deviation =0.6*(4)1/2=1.2

hence P(X<1002.5)=P(Z<(1002.5-1000)/1.2)=P(Z<2.0833)=0.9814

b)here let 4 componets length is A and that of slot is B

hence mean of A-B=1000-1002.5=-2.5

and std error of difference =(1.22+0.42)1/2 =1.2649

hence P(A-B<0)=P(Z<(0-(-2.5))/1.2649)=P(Z<1.9764)=0.9759

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