Applicational Materials sells several pieces of equipment used in the manufacture of silicon-based microprocessors. In 2003 the company filled 130 orders for model a55212. Suppose that the machines fail according to a Weibull law. In particular, the cumulative distribution function F(t) of the time until failure of any machine is given by F(t)  1  e0.0475t1.2 for all t  0, where t is in years.

a. What is the failure rate function for this piece of equipment?

b. Of the original 130 sold in 2003, how many machines would one expect would not experience a breakdown before January 2007? Assume for the sake of simplicity that all the machines were sold on January 1, 2003.

c. Using the results of part (a), estimate the fraction of machines that have survived 10 years of use that will break down during the 11th year of operation [or you may compute this directly if you did not get the answer to part (a)].