- #1
ArcanaNoir
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Homework Statement
A certain industrial process yields a large number of steel cylinders whose lengths are approximately normally distributed with a mean of 3.25 in. and a variance of 0.008 in2. If two cylinders are chosen at random and placed end to end, what is the probability that their combined length is less than 6.55 in.?
Homework Equations
normal distribution: [tex] \frac{1}{ \sigma \sqrt{2 \pi} e^{ \frac{(x- \mu )^2}{2 \sigma ^2}} }
[/tex]
CDF: integrate
[itex] \mu = [/itex] mean
[itex] \sigma = [/itex] standard deviation
[itex] \sigma ^2 = [/itex] variance
The Attempt at a Solution
I'm not sure if a variance of 0.008 in2 implies [itex] \sigma = \sqrt{.008} [/itex] or [itex] \sigma = .008 [/itex].
I also don't know how to set up the problem since there are two cylinders whose length together is less than 6.55. Do I just divide 6.55 in half?
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