# Using the emperical rule, we have to conclude that the machine that is most likely to produce an acceptable cork is?There are two machiens available for cutting corks intended for use in wine...

Using the emperical rule, we have to conclude that the machine that is most likely to produce an acceptable cork is?

There are two machiens 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.

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### 1 Answer

There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with a diameter that is normally distributed with mean 3 cm and a standard deviation 0.10 cm. The second machine produces corks with a mean diameter 3.04 cm and standard deviation 0.02 cm.

Wine bottles are made of the same size and the size of the cork that would fit in each of them should also have the same size. As no information is provided about the diameter of the cork that would fit into each of the bottles a valid assumption that can be made is that a machine producing corks with a lesser variance in diameter would produce a larger number of corks that can be used with the bottles.

As the standard deviation of corks produced by the second machine is only 0.02 cm while that of the corks produced by the first machine is 0.1 cm, the second machine is more likely to produce an acceptable cork.

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