Question

Bolts produced by a machine are acceptable provided that their length is within the range from 5.95 to 6.05 centimeters. Suppose that the lengths of the bolts produced are normally distributed with μ = 6 centimeters and σ = 0.02. What is the probability that a bolt will be of an acceptable length?

Answer 1

So, here you want the probability of 5.95 to 6.05 - which, in terms of the z number, is (6.05-6.00)/0.02. Use that z number to get the probability of something less than 6.05 (that should be relatively simple), and then subtract 0.5 from that to get the probability from 6.00 to 6.05 (because the normal curve is split in half at the mean). Because this normal distribution is symmetrical, you can multiply that last value by 2 to get the probability between the two bounds, each on the opposite side of the mean.