Company ABC always misses the shipment for their lasers to one of her client, due to fluctuations in their demand in last minutes and the manufacturing process for lasers including three steps: submount assembly, module assembly and final test. Parts that successfully pass through one step go on to the next step. Those parts that fail are scrapped.

The weekly demand from Company ABC for lasers has been 500 lasers on average, but it fluctuates (10-20% more sometimes). It is approximately normally distributed, with a standard deviation of 50 lasers per week.

• The submount assembly yield is approximately Normally distributed, with = 80% and = 5%
• The module assembly yield is approximately binomially distributed, with P(pass) = 95%
• The final test yield appears to be evenly distributed between 90% and 100%

Question

• What is the distribution of the difference between supply and demand?