Please answer the entire question in excel if possible.

A supplier is entering into a contract with a manufacturer to deliver a machine in no later than $8$ weeks

from now. Due to uncertainty in availability of parts for the machine, the supplier is not sure when it will

be able to deliver the machine. Also, when the machine is delivered, there is a chance that the

manufacturer will judge it as being of inferior quality. The supplier estimates the probability distribution

of the time it takes to deliver the machine is given as below.

Independently of this the company estimates that the probability of rejection due to inferior quality $0\mathrm{.}15.$

If the machine is delivered at a least a week ahead of time and the manufacturer judges the quality to be

inferior, the supplier will have time to fix the problem $($with certainty$)$ and still meet the deadline.

However, if the delivery is late, or if it is exactly on time but of inferior quality, the manufacturer will not

pay up$.$

The supplier expects the cost of manufacturing the machine to be $$45,000.$ This is a sunk cost that will be

incurred regardless of the timing or the quality of the machine. The supplier also estimates that the cost to

fix an inferior machine depends on the number of weeks left to fix it: $$7500$ if there are three weeks left,

$$10,000$ if there are two weeks left, and $$15,000$ if there is one week left. The manufacturer will pay

$$70,000$ for a machine of sufficient quality delivered on time, but it will pay nothing otherwise. Find the

distribution of profit or loss for the supplier. Then find the mean and standard deviation of this

distribution. Do you think the supplier should sign the contract?

Discrete Pobability Distribution