91Ó°ÊÓ

In a human factor experimental project, it has been determined that the reaction time of a pilot to a visual stimulus is normally distributed with a mean of \(1 / 2\) second and standard deviation of \(2 / 5\) seconds. (a) What is the probability that a reaction from the pilot takes more than 0.3 seconds? (b) What reaction time is that which is exceeded \(95 \%\) of the time?

The length of time between breakdowns of an essential piece of equipment is important in the decision of the use of auxiliary equipment. An engineer thinks that the best "model" for time between breakdowns of a generator is the exponential distribution with a mean of 15 days. (a) If the generator has just broken down, what is the probability that it will break down in the next 21 days? (b) What is the probability that the generator will operate for 30 days without a breakdown?

The length of life, in hours, of a drill bit in a mechanical operation has a Weibull distribution with \(\alpha=2\) and \(0=50 .\) Find the probability that the bit will fail before 10 hours of usage.

Derive the cdf for the Weibull distribution. [Hint: In the definition of a cdf, make the transformation \(\left.z=y^{\beta} .\right]\)