Question: Components that are critical for the operation of electrical systems are replaced immediately upon failure. Suppose that the life time of a certain such component has mean and standard deviation of 100 and 30 time units, respectively. How many of these components must be in stock to ensure a probability of at least 0.95 for the system to be in continuous operation for at least the next 3000 time units? (Hint. If T = X1 +···+ Xn is the combined duration of n components, we want P(T > 3000) = 0.95. This means that 3000 is the 5th percentile of T. Using the CLT to approximate the 5th percentile of T leads to a quadratic equation for the square root of n, that is, an equation of the form αx2 + βx + γ = 0, with x being the square root of n. The roots of such an equation can be found with the R command polyroot(c(γ , β, α)).)