Statistics

Background: A machine cuts wood boards to a thickness of 25 millimeters with an accepter margin of error of +/-0.6 ml. (Assume process can be distributed by normal distribution.) The acceptable range of thicknesses for the boards is 24.4 ml to 25.6 ml, inclusive.

Because of vibration, the machine shifts from 25 ml. To check the machine, you select at random three samples of four boards and find the mean thickness of each.

You select a board. Assume the machine shifts and is cutting boards with a mean thickness of 25.4 ml and a standard deviation of .2 ml.

Question: What is the probability that you select a board that is not outside the acceptable range?

Question: You randomly select 12 boards. What is the probabiliy you select at least one boards that is not outside the acceptable range?

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