The following is the probability distribution of the number of accidents in one day. ___\"n\" mum-n (a) Compute the value of a. (b) Find the probability that at least nine accidents in one day. (c) Find the probability that at most eight accidents in one day. (d) Find the expected value of X. (9) Find the variance and standard deviation of X. A machine produces parts of which 3% are defective. If a random sample of 20 parts produced by this machine contains three or more defectives, the machine is shut down for repairs. Find the probability that the machine will be shut down based on this sampling plan. The number of students coming in complaining of stomach problems during a typical day at the Student Health Centre is Poisson distributed with mean g. If the probability that no student comes in complaining of stomach problems in one day is 0.02. (a) Calculate ,u. (b) Find the probability that more than 3 students come in complaining of stomach problems in 2 days