A manufacturer of wet grinders wants to buy a one-HP motor from a supplier. In a lot of 1000, when fitted to the machine, these motors have a probability of failure 0.001. If X represents the number of failures of an assembled motor, then (a) sketch the probability mass function (roughly), (b) sketch the cumulative distribution function (roughly). Also, Find the probability that 420 motors will fail, (a) at most 630 motors will fail, (b) at least 150 motors will fail, (c) between 160 and 190 motors will fail, (d) mean, (e) Find E(4X + 51.324).

Solve it using R code