Normal Distribution

Anonymous
timer Asked: Jun 22nd, 2018
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Question description

Normal Distribution

One theory about the daily changes in the closing price of a stock is that these changes follow arandom 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 opening and closing prices of stocks from for your favorite company or brand.

Initial Post:

  1. 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.
  2. 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.
  3. Calculate the mean and standard deviation of the daily stock changes by running the Descriptive Statistics in Excel Data Analysis. Share the summary table.
  4. Consider the mean, median and mode (if it exists). Is your daily stock change distribution right skewed (median < mean), left skewed (mean < median), or symmetric (mean ≈ median)? What other considerations would you look at to determine whether or not this distribution is approximately normally distributed?

See Example post.

First response: Read a classmate’s response. Consider investing in your classmate’s stock and assume that the daily change is normally distributed. Using Normal.xlsx, your classmate’s mean and standard deviation, determine the probability for the daily change 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 more 1 point or more (X ≤ -1)?
  4. An increase of more than 1 point (X > 1)?

See Example post.

Second Response: Read a different classmate’s response. Consider investing in your classmate’s stock and assume that it is normally distributed. If you wanted to be 95% sure of what the daily change would be, what range for a daily change would you expect? Use Normal.xlsx.

See Example post.

Unit 3 Discussion Example - First Response to Classmates’ Post First response: Read a classmate’s response. Consider investing in your classmate’s stock and assume that the daily change is normally distributed. Using Normal.xlsx, your classmate’s mean and standard deviation, determine the probability for the daily change 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 more 1 point or more (X ≤ -1)? 4. An increase of more than 1 point (X > 1)? In your own words, explain if these are high or low likelihoods for change. ****************************************************************************** ******* I will review the Crocs, Inc daily stock change. Using the mean = 0.094 and standard deviation of 0.14378865 and Normal.xlsx: 1) P (X ≤ -0.5) = 0.0098 = 0.98% 2) P (X > 0.5) = 0.0539 = 5.39% 3) P (X ≤ -1) = 0.00 = 0% 4) P (X > 1) = 0.0002 = 0.02% Common Data Common Data Mean 0.0922581 Mean 0.0922581 0.2535838 Standard Deviation 0.2535838 Standard Deviation Probability for X <= Probability for X <= -1 X Value -0.5 X Value Z Value -2.335552 Z Value -4.307287 P(X<=-0.5) 0.0098 P(X<=-1) 0.0000 Probability for X > X Value Z Value P(X>0.5) 0.5 X Value 1.6079181 Z Value 0.0539 P(X>1) Probability for X > 1 3.5796531 0.0002 Comparing thefor decrease of 0.5 points or more, it is more likely to increase (5.39%) Probability X<-0.5 ororX increase >0.5 than to decrease P(X<-0.5 or X >0.5)(0.98%). 0.0637 Comparing the decrease or increase of 1 point or more, it is more likely to increase however; it is a very low likelihood that the stock would change 1 point (only 0.02%).
Unit 3 Discussion Example - Second Response to Classmates’ Post Second response: Read a different classmate’s response. Consider investing in your classmate’s stock. If you wanted to be 95% sure what the daily change would be, what range for a daily change would you expect? Use Normal.xlsx. ************************************************************************************* I will review the Crocs, Inc daily stock change for June 1 – July 15, 2016. With 95% probability, I would expect the daily change in the stock price to be between -0.40 and 0.59 points. Find X Values Given a Percentage Percentage 95.00% Z Value -1.96 Lower X Value -0.40 Upper X Value 0.59

Tutor Answer

mickeygabz
School: UT Austin

See attached

Discussion post: Facebook
For my stock, I chose Facebook. I chose the company because of the data privacy issues
surrounding it and I wanted to investigate how the issues were affecting its stock price.
The data collected was based on the past 6 weeks and is shown below:
Daily
Date
Open
Close
change
5/8/2018 178.25 178.92
0.67
5/9/2018 179.67 182.66
2.99
5/10/2018 183.15 185.53
2.38
5/11/2018 184.85 186.99
2.14
5/14/2018 187.71 186.64
-1.07
5/15/2018 184.88 184.32
-0.56
5/16/2018
183.7
183.2
-0.50
5/17/2018 182.68 183.76
1.08
5/18/2018 183.49 182.68
-0...

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Review

Anonymous
Thanks, good work

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