Amy is a consultant who has provided three different training options to a client. If the client chooses option (a), Amy will have to hire one additional employee. If the client chooses option (b), she will hire 2 new employees, and if option (c) is chosen, she will need to hire 4 additional employees. Amy estimates the probability that the client will chose option (a) to be 0.20, with P(b)=.35 and P(c)=.15.
a. What is the probability that the client will decide not to accept any of the three options, that is, what is the chance Amy will not have to hire any new employees?
b. Create a table for the probability distribution for the random variable X, the number of new employees Amy will have to hire.
c. Compute the expected value of the number of new employees Amy will hire for this client.
d. Compute the standard deviation of the number of new employees Amy will hire for this client.