There are two machines available for cutting corks intended for use in wine bott

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 3 cm and standard deviation 0.08 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 What is the probability that the first machine produces an acceptable cork? (Round your answer to four decimal places.) What is the probability that the second machine produces an acceptable cork? (Round your answer to four decimal places.) Which machine is more likely to produce an acceptable cork? the first machine

Explanation / Answer

First machine mean = 3 , s = 0.08

second machine mean = 3.04 , s = 0.02

P(2.9 < x < 3.1)
= ((2.9 - 3) /0.08 < z < ( 3.1- 3.04) / 0.02)
= (-1.25 < z < 3)

P(2.9 < x < 3.1) = P(-1.25 < z < 3) = P( 3.1) - P( 2.9)

= 0.9987 - 0.8944 = 0.1043

Machine 2 is more likely to produce an acceptable cork

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