There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3cm and standard deviation 0.10cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04cm and standard deviation 0.02cm. Acceptable corks have diameters between 2.90cm and 3.10cm. Using the emperical rule, we have to conclude that the machine that is most likely to produce an acceptable cork is

a)machine 1: it has approximately 68% success, compared to 50% on machine 2.
b)machine 1: it

Question

There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3cm and standard deviation 0.10cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04cm and standard deviation 0.02cm. Acceptable corks have diameters between 2.90cm and 3.10cm. Using the emperical rule, we have to conclude that the machine that is most likely to produce an acceptable cork is

a)machine 1: it has approximately 68% success, compared to 50% on machine 2.
b)machine 1: it

dumbcow · Answer

machine 2 is more likely to produce an acceptable cork because it has a much smaller standard deviation
machine 1 has 68% chance, machine 2 has 99% chance

anonymous · Answer

how did you calculate?

dumbcow · Answer

machine 1; 2.9 = 3 -.1 = mean -std dev
                  3.1 = 3+.1 = mean +std dev
on the normal distribution curve, 68% probability of being within 1 std dev

machine 2:  2.9 = 3.04 -.14 = mean -7std dev
                   3.1 = 3.04 + .06 = mean +3std dev
on the normal distribution curve, 99% probability of being within 3 std dev