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 3 cm and standard deviation 0.1 cm. the second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.02 cm. acceptable corks have diameters between 2.9 cm and 3.1 cm. which machine is more likely to produce an acceptable cork

Question

Mathematics

Marcel

18 February, 17:40

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 3 cm and standard deviation 0.1 cm. the second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.02 cm. acceptable corks have diameters between 2.9 cm and 3.1 cm. which machine is more likely to produce an acceptable cork

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Darrell Ayala · Answer 1

The first machine produces an acceptable cork with probability 68.3%. The second machine produces an acceptable cork with probability 99.9%.

The second machine is much more likely to produce an acceptable cork.