You work for a pharmacuticals company as a statistical process

You work for a pharmacuticals company as a statistical process analyst. Your job is to analyze processes and make sure they are in statistical control. In one process, a machine is supposed to add 9.8 mg of a compound to a mixture in a vial. (assume this process can be approximated by a normal distribution.) The acceptable range of amonts of the compound added is 9.65 mg to 9.95 mg inclusive.

Because of an error with the release valve, the setting on the machine shifts from 9.8 mg to check that the machine is adding the correct amount of the compound into the vials, you select at random 3 samples of 5 vials and find the mean amount of the compound added for each sample. A coworker asks why you take 3 sample of size 5 and find the mean instead of randomly choosing and measuring the amounts in 15 vials individually to check the machine settings (note: both samples are chosen without replacement)

  1. You select one vial and determine how much of the compound was added. assume the machine shifts and the distribution of the amount of the compound added now has a mean of 9.96 mg and standard deviation of 0.05 mg (A) What is the probablity that you select a vial that is not outside the acceptable range? (B) You randomy select 15 vials what is the probability that you select at least one vial that is not outside the acceptable range?
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