Continuous probability distributions: Procurement and working capital analysis – Normally distributed random variables and their transformation

Procedures

The data is measured in unites, so will have to transform a normally distributed random variable by multiplying it by a constant factor.

Following that transformation, will be required to sum 30 independent, identically distributed random variables to evaluate working capital needs for the month.

Q1

You have been given the following task by the VP of Manufacturing at Telsa to assess the capital needs of the supply chain.

“One of most expensive components in our cars is an internal control module (ICM) that allocates power to different systems: communication, climate, drive, etc. Our supplier charges us about $5,000 each and delivers them on a Just-In-Time basis. I want to know the distribution of delivery of these units each day so that I can assess my storage needs. I also need to know the distribution of our expenditures for ICMs, so I can assess my working capital needs. I will need a recommendation from

you.”

Prepare a memorandum for the VP (no more than 3 pages) that characterizes the number of distribution of the number of units being delivered and the daily expenditure for ICMs. You should provide graphical as well as a numerical analysis. You may assume that the distribution is normal. If working capital is allocated every month (30 days), make a recommendation on the WC needs for procurement of ICMs. Justify your recommendation.

Q2: What are the quartiles of the distribution of ICMs needed each day?

Q3: What are the quartiles lf the ICM working capital distribution?

Q4: What is the probability that the daily need for ICMs is less than 100? More than 150?

Q5: What is the probability that the daily WC need is more than $600,000? Less than $400,000?

Q6: What is the probability that a WC allocation of $20 million for ICMs at the beginning of the month is inadequate?