## (Solved) Due to many factors, such as slight variations in the metal, different operators and differentmachines, the thickness of metal plates manufactured in...

Due to many factors, such as slight variations in the metal, different operators and differentmachines, the thickness of metal plates manufactured in a factory varies and can beconsidered as a normal random variable with mean Âµ = 20 mm and standard deviationÏƒ = 0.04 mm.(a) How much scrap can be expected if the thickness of the metal platesi. has to be at least 19.95 mm?ii. can be at most 20.10 mm?iii. can differ at most by 0.05 mm from the target 20 mm?(b) If four metal plates are selected at random, what is the probability that two or moremetal plates have thickness less than 19.95 mm?(c) Suppose that 100 metal plates are purchased from this manufacturer and the thicknessof each metal plate is measured individually. If the thickness is found to be lessthan 19.95 mm, 10% less is paid to the manufacturer for that metal plate. If thenormal price of a metal plate is \$50, what is the expected cost of 100 metal plates?(d) How would the manufacturer have to set the tolerance limits 20 âˆ’ c and 20 + c suchthat the factory produces at most 5 percent metal plates that fall outside the limits?(e) Assume that the mean has shifted to Âµ = 20.10. Calculate the percentage of metalplates that do not conform to the tolerance limits in part (d).

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