A machine produces bolts which are N (4, 0.09), where measurements are in mm. Bolts are
measured accurately and any which are smaller than 3.5mm or bigger than 4.4mm re rejected. Out of
a batch of 500 bolts, how many would be acceptable?
Answers
Given : A machine produces bolts which are N (4, 0.09), where measurements are in mm.
Bolts are measured accurately and any which are smaller than 3.5mm or bigger than 4.4mm re rejected.
To Find : Out of a batch of 500 bolts, how many would be acceptable
Solution:
N (4, 0.09)
Mean = 4
SD = 0.09
Z score = ( Value - Mean)/SD
smaller than 3.5mm
( 3.5 - 4)/0.09 = 5.55
bigger than 4.4mm
( 4.4 - 4)/0.09 = 4.44
Z scores are too high that in a batch of 500 bolts none will be found rejected
Hence 500 will be acceptable.
considering 0.09 as variance then SD = 0.3
smaller than 3.5mm
( 3.5 - 4)/0.3 = -1.667
=> 4.77 %
bigger than 4.4mm
( 4.4 - 4)/0.3 = 1.33
=> 90.87%
Acceptable = 90.87% - 4.77 %
= 86.1 %
= ( 86.1/100) * 500
= 430.5
= 431 bolts will be accepted
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