3. (15 points) There are two machines available for cutting corks intended for use in bottles. The rst produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.1 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.05 cm and standard deviation 0.05 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. (3) Which machine is mole liker to produce an acceptable cork? (6 points) (b) What should the acceptable range for cork diameters be (from 3 d cm to 3 + dcm) to be 95% certain for the rst machine to produce an acceptable cork? (9 points)