A certain type of circuit board manufactured for installation in computers has 1

Question

A certain type of circuit board manufactured for installation in computers has 12 microchips per board. During the quality control inspection of ten of these boards, the numbers of defective microchips on each of the ten boards were as follows: 2, 0, 1, 3, 2, 0, 0, 1, 3, 4 (a) Estimate the proportion of defective microchips in the population from which this sample was drawn and place a bound on the error of estimation. (b) Suppose the sample of ten boards used there came from a shipment of 50 such boards. Estimate the total number of defective microchips in the shipment and place a bound on the error of estimation.

Explanation / Answer

a)total number of defective microchips =16

total microchips =12*10=120

hence proportion of defective microchips =16/120=0.1333

b) estimated number of defective chips =0.13333*50*12=79.998~80

and std deviaiton =(np(1-p))1/2 where n=12*50=600 chips

=8.327

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