This sounds good, you have to use the 68%-95%-99.7% rules here or look up a table. This online calculator will help.
Z table - Normal Distribution
A cylinder is to be machined to a diameter of 8cm. The Upper specifications limit is 8.2cm and the lower specifications limit is 7.9cm. A certain machine produces cylinders with a mean of 8.1cm with a standard deviation of 0.1cm.
What is the probability of being outside the tolerances for the cylinder?
I know P(X>8.2) and that i then need to convert it to a Z score with z=X-mean/Standard Deviation = z=8.2-8.1/0.1 = 1
I get stuck from there.
Any help would be greatly appreciated
This sounds good, you have to use the 68%-95%-99.7% rules here or look up a table. This online calculator will help.
Z table - Normal Distribution
Maybe your z-tables only deal with positive values of z.
The probability of being outside the tolerances is P(z<-2)+P(z>1), since
The values given by the z-tables are P(z<value) or
which are basically the same as the curve is continuous.
However P(z<-2)=P(z>2) due to the symmetry of the bell-shaped curve.
and P(z>2)=1-P(z<2)
Also P(z>1)=1-P(z<1)
Hence the probability of being machined outside of specifications is
So
<--- probability of being machined above the specifications
<--- probability of being machined lower than the specifications
Then add the two probabilities to get the probability of being machined outside of the specifications.
Is this right???
Yes,
that's what I get also.
You're calculating the probability of z being between 0 and 1
then subtracting from 0.5 to get the probability of being above 1....
and z being between 0 and -2
and subtracting from 0.5 to find the probability of z being below -2.
Excellent.