SOLUTION: A cutting machine cuts lengths of steel with a standard deviation of 2mm. The machine is set so that the mean length is 3000 mm. The lengths are approximately Normally distributed.

Question 1157340: A cutting machine cuts lengths of steel with a standard deviation of 2mm. The machine is set so that the mean length is 3000 mm. The lengths are approximately Normally distributed. In one run, the machine cuts 500 lengths. On average, how many would you expect to be less than 2997.5m mm long?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd
=(2997.5-3000)/2
that is -2.5/2=-1.25
probability of z < -1.25 is 0.1056
so the number of lengths fewer than 2997.5 mm long is the product of the prob and the number 500 or 52.8. I would expect 53 on average to be in that group.
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