• Show your work and explain your process for determining the solution for each of these problems on a word document with the solution given below the problem.
• If Excel was used, please indicate that as well on the word document.
• A word document and/or the Excel Workbook (if used) should be submitted to the Dropbox with labels on the worksheets to indicate which problem is being evaluated.
• All answers should be clearly indicated.
• Written explanation, reasoning, and rationale should use complete sentences.
One theory about the daily changes in the closing price of a stock is that these changes follow a random walk – that is, these daily events are independent of each other and move upward or downward in a random manner – and can be approximated by a normal distribution. To test this theory, collect the most recent closing prices of stocks for your favorite company or brand. You can find this by going to finance.yahoo.com and searching for “Your Company stock history.” See Example and CA Starter video in this module’s LiveBinder.
Part 2A Solve real world problems using mathematics.:
1. Learn the properties of a probability distribution.
a. Choose your favorite company or brand and search finance.yahoo.com with that company name and “historical stock prices”. Download the stock history for this company for the past 6 weeks by selecting the appropriate dates and clicking on “Download to Spreadsheet” at the bottom of page.
b. Calculate the daily change in the closing stock prices by taking the difference between the closing and opening price for the day. This is the daily stock change.
c. Run the Descriptive Statistics->Summary Table in Excel Data Analysis on the daily stock change. Share the summary table.
d. Calculate the 1st and 3rd quartiles of the daily stock change. Share these along with the min, median, and max from 3) as your 5-Number Summary.
e. Create a Box & Whiskers Plot using your 5-Number Summary. (For Help, refer to M305M1’s LiveBinder).
f. Is your daily stock change distribution right skewed (median < mean), left skewed (mean < median), or symmetric (mean ≈ median)?
2. Identify normal probability distributions.
a. Would you consider your daily stock change to be normally distributed? Why or Why Not?
Part 2B: Solve problems using the Central Limit Theorem and Apply the sampling distribution of the mean.
Consider investing in your stock and assume that the daily change is normally distributed. See Example and use Excel template found in LiveBinder. Using your mean and standard deviation, determine the probability for the average of 9 daily changes of this stock to have:
1. A decrease of 0.5 point or more (X ≤ –0.5)?
2. An increase of more than 0.5 point (X > 0.5)?
3. A decrease of 1 point or more (X ≤ –1)?
4. An increase of more than 1 point (X > 1)?
5. In your own words, explain if these are high or low likelihoods for change.
Part 2C: If you wanted to be 95% sure what the daily change would be, what range for a daily change would you expect? Use the appropriate worksheet located in the workbook found in LiveBinder.
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