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Answer: 0.7887
Step-by-step explanation:
Let x be the random variable that represents the diameters of the corks .
Given : The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.08 cm.
i.e.
Acceptable corks have diameters between 2.9 cm and 3.1 cm.
Then, the probability that the first machine produces an acceptable cork will be :_
∴ The probability that the first machine produces an acceptable cork= 0.7887