Question 1092412
z=(x-mean)/sd
each x is +/- 0.2 when the mean is 36 and divided by the sd of 0.1, z is between -2 and 2, which has probability of in control is 0.9545.
P(out of control)=0.0455.
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b.  That would be 0.9545^16=0.4747.
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c. This would be 16 ways to be 1 and 15 ways to be 0 so 16*0.0545*0.9545^15=0.3620
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d. To be out of control I am assuming the bottle should be between 35.8 and 36.2 still
that would be a z of (35.8-37)/0.4=-3 to (36.2-37)/0.4=-2. That would be .0214 probability in control and 0.9786 out of control. I'm not sure what the new limits are.