• 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.

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.comand searching for "Your Company stock history."

Part 2A Solve real world problems using mathematics.:

1. Learn the properties of a probability distribution.
   1. Pick 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 the page.
   2. what is 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.
   3. Run the Descriptive Statistics->Summary Table in Excel Data Analysis on the daily stock change. Share the summary table.
   4. what is 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.
   5. build a Box & Whiskers Plot using your 5-Number Summary.
   6. Is your daily stock change distribution right-skewed (median < mean), left-skewed (mean < median), or symmetric (mean median)?
2. what are the normal probability distributions?
   1. Would you consider your daily stock change to be normally distributed? Why or Why Not?

Part 2B:Use the Central Limit Theorem and Apply the sampling distribution of the mean.

Think about investing in your stock and assume that the daily change is normally distributed. Usingyour 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. communicate 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?