1. Let X represent the lifetime of a component in a piece of lab equipment, and suppose that X is exponentially distributed with a mean of µ = 1000 hours.
(a) Sketch the density function of X .
(b) Find P( X 1000).
(c) Find P( X 5000).
(d) Find P( X > 100).
(e) Find P( 50 X 250).
(f) Find the goth percentile of X .
(g) Why might this information be important to the lab personnel?
2. The stability of a paint was tested by subjecting it to increasing times at a high temperature. The viscosity of the paint was used to determine the point of failure (when the viscosity is too high the paint is said to have gelled and is no longer usable). The time until the material gelled is given for 17 samples in viscosit y .txt.
(a) Construct a histogram for these data.
(b) The test was designed assuming the time to failure would be exponen tially distributed. Estimate the parameter of the exponential distribution, and write down the resulting estimated distribution function.
(c) Use your answer from part (b) to estimate the probability that the paint would gel in less than 4.5 days.
(d) Find the 10th percentile of the distribution, and explain what it stands for.
(e) Another engineer in looking over the results says "These numbers must be wrong. With normal use, we would expect the paint to last for years, while most of these samples failed in a matter of days." Explain the seeming paradox.