4.) a.) Many cylinders are to be produced for a laboratory application. Suppose

Question

4.)
a.) Many cylinders are to be produced for a laboratory application. Suppose that the thickness of a cylinder has a normal distribution with a mean of 1.41 cm and a standard deviation of 0.01 cm. What is the probability that the thickness is greater than 1.42 cm?

b.) For the cylinder described in part a., what thickness is exceeded by 95% of the samples?

Explanation / Answer

Given X~Normal(mean=1.41, s=0.01) ----------------------------------------------------------------------------- (a) P(X>1.42) = P((x-mean)/s > (1.42-1.41)/0.01) =P(Z>1) = 0.1587 (check standard normal table) ----------------------------------------------------------------------------- (b) P(X P(Z (c-1.41)/0.01 =1.645 (check standard normal table) --> c= 1.41 +0.01*1.645 =1.426

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