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The operation manager of a large factory in China wishes to implement a quality control in the assembly process of a sub-component of a plasma television. Such control is believed to enhance workers' efficiency. This will then lead to an improvement in profit. The amount of time required to assemble the sub-component is normally distributed, with a mean of 15 minutes and a standard deviation of 1.8 minutes.
a) What is the probability that one randomly selected assembly would take at most 17 minutes to complete? Display working.
b) The 10% assemblies which take the longest to complete would at least require how much time (in minutes)? Display working.
c) The operation manager randomly selected seven assemblies. What is the probability that the mean amount of time taken to complete those seven assemblies is more than 15.6 minutes? Display working.
d) In further implementing the quality control, eight other assemblies are randomly selected. What is the probability that the average amount of time to complete those eight assemblies is between 15 minutes and 16 minutes? Display working.
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