Mathematics Homework Help

Learning Goal: I’m working on a probability question and need support to help me learn.

A
statistical process control chart example. Samples of 20 parts from a
metal punching process are selected every hour. Typically, 1% of the
parts require rework. Let X denote the number of parts in the sample of
20 that require rework. A process problem is suspected if X exceeds its
mean by more than three standard deviations.

Does this scenario adhere to the requirements to be binomial? Explain.

Calculate the mean. Does it make practical sense? What about the variance?

Part
(a) of this exercise asks: If the percentage of parts that require
rework remains at 1%, what is the probability that X exceeds its mean by
more than three standard deviations? Show how this determined. Now
answer: does this make “real world” sense?

As a supervisor, how
would you retool your statistical process control data gathering to be
more informative? What considerations will you make?