The Weibull distribution is often used in engineering studies to model the random lifetime of a device. It is a right-skewed distribution and can be generated with the RiskWeibull function. This function takes two positive parameters, alpha and beta, that determine he shape and location of the distribution. Consider a piece of equipment that contains a battery with a Weibull-distributed lifetime (in days) with parameters alpha = 2 and beta = 80. (It can be shown that the mean and standard deviation of this distribution are about 70 and 37.) NASA is about to send this piece of equipment into space, where its mission is to last at least 600 days. The equipment will be accompanied by one battery and n-1 standby spare batteries, that is, n batteries total. When a battery fails, it will automatically be replaced by a spare, at least as long as there are any spares left.
a. Use simulation to estimate the probability that the equipment will accomplish its mission if n = 10 batteries are supplied.
b. Although the probability from part a is reasonably large, NASA wants it to be even higher. Use simulation to find the value of n so that the equipment will accomplish its mission with probability at least 0.99.