Homework Assignment 5

1. What kind of price/probability distribution are you assuming based on the information in the previous paragraph? (Ahem. The answer to this ought to be automatic after the last homework assignment.)
2. Explain why you gave the answer you gave to (A).
   Next, make a chart that schematically shows the distribution you answered in question (A). Note. This chart will not come from actual data. It comes from your answer to (A). Be sure to put in the important numbers on the X and Y axes. From the last homework assignment you know you can make the chart in several ways. Use whatever method you prefer. Show some "zero probability" space on each side of the distribution to make your chart clear. For example, have x run from $1 to $5 per 12 ounces.
3. What is the theoretical standard deviation of the distribution you used above? Bold your numerical answers using a 14-point font.
   Now, just for fun, you want to generate a set of price data that fits the distribution in (A). Use Excel like you learned in the last homework assignment. Generate a matrix of 9000 price numbers that are in the appropriate range. Each random number should be put in one of 30 columns and 300 rows.
   Now your boss comes in and says she likes your work so far but wants you to take it another step. It seems she had a friend that worked for Wal-Mart and her friend said Wal-Mart’s policy on regional foodstuffs like boudin is to first run price experiments for six months and then use the information from those experiments to set their prices to maximize their long term profit. Their procedure is to use a statistical technique. On a weekly basis the price is set by randomly selecting 30 possible prices (which you have to assume will come from the distribution you have defined above) and then they use the average value for the whole week. This procedure keeps their intentions secret and confuses the competition. So, you want to show your boss a picture of the possible pricing pressure your company will be facing given this new information. You need to make two histograms.
   First, make a histogram of the 9000 numbers you have already generated. Use bins of $1.00, $1.10, …, $5.00 so all of your charts will have similar x axes. Label your histogram with the name of the appropriate distribution. Make sure you clearly label your histogram. What are you going to use for a label on the X-axis? Will your boss know what "bins" means? No. Do you want to make your boss have to ask? No. Take care of your boss and he or she will take care of you.
4. What is the standard deviation of the 9000 numbers? Bold your numerical answer using a 14-point font.
   Second, find the average of the 30 numbers in each of your 300 rows of data. This gives you 300 sample averages from your 9000 random numbers, where each average is based on 30 numbers. Make a histogram of these averages using the same bins used for the first histogram. (Incidentally, you would make these bins smaller if you were making only this histogram, but since we want to compare the two histograms we need to use the same x-axis scale.)
5. What is the name of the distribution that is emerging in the second histogram?
6. Calculate the standard deviation (standard error) of the 300 averages using two fundamentally different methods . One method should be theory-based and the other should use the numbers you have generated. Clearly explain each method you use. Show your formulas and show the numbers you plug in. Bold your numerical results using a 14-point font.

Extra Credit: What is the probability that during any random week Wal-Mart’s price will be less than $2.65 per 12 ounces?

Price: $14.4

Solution: The downloadable solution consists of 6 pages, 840 words and 3 charts.
Deliverable: Word Document