68-95-99.7 rule

Question

A company makes for a machine. The lengths   of the part must be within certain limits or they will be rejected. A large   number  of parts were measured with the mean and standard deviation  calculated as 10.4 inches and 0.016 inches respectively. Assuming  the data is normally  distributed and 99.7% of the parts were accepted, what are the limits for the size of the parts? Don't round

Answer 1

The 68-95-99.7 rule says that, in a set of normally distributed data, 68% of data is within one standard deviation of the mean, 95% is within two standard deviations of the mean, and 99.7% is within three standard deviations of the mean.

 

So, 99.7% of the parts are within three standard deviations of the mean. In other words, they were between 10.4 - 3(0.016) inches and 10.4 + 3(0.016) inches. Those values are:

 

10.4 - 3(0.016) = 10.4 - 0.048 = 10.352 inches

10.4 + 3(0.016) = 10.4 + 0.048 = 10.448 inches