SDS 03. A machine which is supposed to produce bearings of a specified diameter is periodically checked for accuracy. From past experience it is felt...

Chapter :Sampling distribution

Ans D

Could you explain me the answer in detail with workings.

SDS 03. A machine which is supposed to produce bearings of a specified diameter is periodicallychecked for accuracy. From past experience it is felt that the diameters should be normallydistributed and have a standard deviation of .010 inches. However, as certain settings onthe machine periodically slip, the mean diameter u is considered to be unknown. If a randomsample of 25 bearings is selected, what is the probability that the average of theirbra 25 nesmdiameters will be within .004 inches of u?w noltelug80 2012(A) .8904malessolqmse mrobes(B) .3108(C) .4772dodong (D) .9544(E) essentially 1.000