Math and stat

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2)Peter is a manager of a bottle manufacture factory. The diameter of a bottle is normally distributed with mean 8 cm and standard deviation 0.08 cm. Aproduced bottle will accepted only if the diameter is not more than 8.12cm and not less than 7.96cm. Any unaccepted bottle will be destroyed.

a.What is the probability that a randomly selected bottle will be accepted?

b.Each accepted bottle will be sold at $0.02. If the produation cost for 100000bottles are$500, what is the expected revenue for producting 500000 bottles.

c.The quality of the produced bottle can be improved by replacing the existing machine with a new one. With the new machine, the diameter of a bottle will follow a normal distribution with mean 8.04cm and standard deviation 0.04cm. What is the probability that a randimly selected bottle produced by the new machine will be accepted?

d.Petre wants to find the value of L such that (8.04-L,8.04+L)cm will contain 95% of the diameters of the bottles produced by the new machine. What is the value of L?