There are two machines available for cutting corks intended

There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diam- eters that are normally distributed with mean 3 cm and stan- dard deviation .1 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation .02 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. Which machine is more likely to produce an acceptable cork?

Solution

The first machine is not more likely to produce acceptable corks because the range 2.9-3.1 is only one standard deviation in each direction away from the mean. That only accounts for 68% of the data.

The second machine needs at least three standard deviations in each direction to reach the maximum acceptable range, and three standard deviations accounts for 99.7% of the data.

Hope this helps! :) Let me know if you have any other questions.