Distribution Assignment | Professional Writing Services

1.1 Uncertainty in Supply Chains (Normal Distribution)

Suppose that daily demand for bagels at the local coffee shop where you work is found to be Normally distributed with a mean of 250 and a standard deviation of 75 units.

1.1 Suppose you have 350 bagels ready to sell on a certain day. What is the probability that you will run out? That is, what is the probability that the demand is greater than 350 on a certain day?

1.2 This is not good enough for you! How many bagels do you need to prepare to have only 5% probability of running out?

1.3 You want to be even surer that you do not run out of bagels! How many bagels do you need to prepare to have only 1% probability of running out?

1.4 You make an interesting observation. Keeping 350 bagels ready to sell provides you with about a 90% probability of not stocking out. Increasing this by 23 bagels improves this probability of not running out to 95%! However, to get this just 4% higher, it takes 52 additional bagels!! Why is this?

a)   Bagels do not follow normal probability rules

b)   The long tails of the Normal Distribution make it increasingly hard to improve upon high levels of service.

c)   The Poisson Distribution is more appropriate

d)   The Normal Distribution has a naturally skewed distribution to the right that creates a long tail

2. Cakes at the Bagel shop (Poisson Distribution)

At the bagel shop, you have some cakes that you sell that are pretty slow movers. The chocolate cake, for example, only sells on average 2.5 cakes per week. You have noticed that the demand follows a Poisson distribution.

2.1 What is the probability that you will sell more than 3 cakes in a week?

2.2 What is the probability that you will sell no cakes in a week?

2.3 Suppose you have 5 cakes made ready to sell. What is the probability that you will sell out?

3. Himmat’s Computer Shop (Uniform Distribution)

Himmat’s Computer Shop is a computer parts wholesaler. Himmat’s buys computer parts in bulk, breaks shipments down into smaller quantities and then sells these smaller quantities to various computer repair shops around the region. Himmat’s receives 45% of their computer parts from Foxconn.

Deliveries from Foxconn arrive every morning. The Foxconn delivery driver is inconsistent and arrives at a uniformly distributed time between 07:02 AM and 07:46 AM.

3.1 What is the probability that a Foxconn delivery arrives before 07:17 AM?

3.2 What is the probability that a Foxconn delivery arrives after 07:11 AM but before 07:39 AM?

4. Jarvis Systems (Triangle distribution)

Jarvis Systems, a smaller supplier, also ships to Himmat’s on a regular basis. Since, Himmat’s doesn’t rely heavily on Jarvis Systems as a supplier, they don’t bother keeping track of the time the Jarvis driver shows up. The Jarvis Systems driver never arrives before 9:15 and always arrives before 10:20. He normally shows up around 9:50.

4.1 Using the Triangle distribution, how often does the Jarvis driver show up before 9:45 AM?

4.2 Using the Triangle distribution, how often does the Jarvis driver show up After 9:30 AM?