# Mathematics

**Project 3 instructions**

**Based on Larson & Farber: sections 5.1–5.3**

Go to http://www.google.com/finance/historical?cid=694653&startdate=Nov+20%2C+2011&enddate=Nov+18%2C+2012&num=30&ei=JaipUPDLIIK10QH57wE

Click the link on the right that says *Download to Spreadsheet*. Set the date range to end on 11/19/13 (the beginning of Module/Week 5) and going back exactly 1 year (11/20/12). Then, click the link on the right that says, “Download to Spreadsheet.” Assume that the closing prices of the stock form a normally distributed data set. (Now will be a good idea to review the definition and properties of a normal distribution on p. 236)

Do not manually count values in the data set, but use the ideas found in sections 5.2–5 .3. (You may want to review how to find mean and standard deviation given a data set. It will also help to review how to use Excel to find those quantities. Please refer to the Excel file I posted on DB>>Useful files) Complete this assignment within a single Excel file. Show your work where possible.

Answer the following:

- If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? Hint: Use the Empirical Rule, do not calculate the mean. The answer is easy.

Hint: use property #2 on p. 236- the normal curve is bell-shaped and is symmetric about the mean.

2. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at more than $500? Hint: Use Excel to find the mean and standard deviation. Then find the z score.

Hint: To find that, you will need to find: a) the mean, b) find z score (let’s call it z1) that corresponds to x = 500, c) find P(z< z1), and recall that P(z > z1) = 1 – P(z<z1)

3. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed within $45 of the mean for that year? Hint: Find two z scores and use the Standard Normal Table.

Hint: Find the z-scores that correspond to adding and subtracting $45 from the mean. Find the corresponding probabilities and then subtract.

4. Suppose a person within the last year claimed to have bought Google stock at closing at $700 per share. Would such a price be considered unusual? Explain by using the Empirical Rule, do not find the max or min values of the daily closing prices

Hint: find the z score. What z score do we say that the corresponding data point x is unusual?

5. At what price would Google have to close at in order for it to be considered statistically unusual? You should have a low and high value. Use the Empirical Rule.

Hint: You will have an upper bound and a lower bound. You will need to find the standard deviation of the data set before you proceed.

6. What are Q1, Q2, and Q3 in this data set? Use Excel to find these values.

Hint: use = quartile(array, 1) to find Q1, =quartile(array, 2) to find Q2, and =quartile(array, 3) to find Q3. The array is your data set.

7. Is the assumption that was made at the beginning valid? Why or why not? Hint: Construct a histogram.

Hint: Does the data set have the properties of a normal distribution? Is the mean and median almost the same? Is the difference between Q1 and Q2 and the difference between Q2 and Q3 approximately the same?