Activity 18.1

In this activity, you will explore some ideas of probability by using Excel to simulate tossing a coin and throwing a free throw in basketball.

1. Toss a coin 10 times and after each toss, record in the following table the result of the toss and the proportion of heads so far. For example, suppose you obtain the following sequence of heads and tails for the first five tosses: H T T T H. After the first toss, the proportion of heads so far is one out of one: \(\frac{1}{1}\) or 1. After the second toss, the proportion of heads so far is one out of two: \(\frac{1}{2}\). After the third toss, the proportion of heads is one out of three: \(\frac{1}{3}\). After the fourth toss, the proportion of heads is one out of four: \(\frac{1}{4}\). After the fifth toss, the proportion of heads is two out of five: \(\frac{2}{5}\).
2. On the following axes, plot the proportion of heads so far, for each toss from your table. What does the graph show?
   Now, you will use Excel to simulate 1000 independent tosses of a fair coin and plot on a graph the proportion of heads so far after each toss using the instructions that follow #3.
3. In Excel, the function RANDO) (that is, RAND followed by two parentheses) produces a decimal number between 0 and 1 , in such a way that every decimal number between 0 and 1 is equally likely to be produced. You will use the RAND() function to generate integers 0 or 1 with equal probability. The integer 1 will signify "heads" and the integer 0 will signify "tails." To get a 0 or 1 with equal probability, you'll multiply the random number by 2 and then take the integer part of it; that is, you will drop all digits after the decimal point.
   Suppose the decimal number produced is 0.13061. What value do you get if you multiply that number by 2 and then take the integer part of it?
4. Write a paragraph explaining what your graph shows.
5. Put the cursor in any blank cell near your graph. Press Ctrl= to change the random numbers and your graph. Do this several times and describe how the graph changes.
6. Shaquille O'Neal is not particularly good at free throws. He makes about 50 percent of his free throws over an entire season.

1. Go to sheet 2 and set up a new worksheet to simulate 100 free throws shot independently by a player who has probability 0.5 of making each shot. In column A, keep a record of the attempt number by generating integers 1 , \(2, \ldots, 100\) in cells A 2 through A101. (Enter an appropriate title in cell A1.)
2. Label cell B1 Hit or Miss and generate a random sequence of $1 s$ (each 1 represents a hit) and 0 s (each 0 represents a miss) in cells B2 through B101.
3. Compute the overall proportion of hits by calculating the mean of the B column values. Also look at your data and identify the length of the longest streak of hits and the length of the longest streak of misses. Write a paragraph commenting on the proportion of hits and the "streaks."

7. A certain college's men's basketball team is quite accomplished at making free throws. According to the coach, in their most recent season the team made approximately 75 percent of free-throw attempts, and ranked $10^{\text {w }}$ in the country among similar schools in successful free-throw attempts.

1. Set up another new worksheet to simulate 100 free throws shot by team members who have probability $0.75$ of making each shot.
2. Again, use column A to keep track of the attempt number in cells A 2 through A101.
3. Label cell B1 Hit or Miss. Now you will generate a sequence of equally likely occurrences of the numbers $0,1,2$, or 3 with 0 representing a miss and any of the other three numbers representing a hit. By entering the formula =INT(4.RAND ()$)$ into cell B2, you can set the sequence up so each of the numbers occurs with equal probability. Then autofill to cell B101.
4. In cell \(\mathrm{C} 2\), enter the formula \(=\mathrm{IF}(\mathrm{B} 2=0,0,1)\). This will give you a " 1 " in cell \(\mathrm{C} 2\) if cell \(\mathrm{B} 2\) recorded a hit, and \(\mathrm{a}^{*} 0^{*}\) if cell \(\mathrm{B} 2\) recorded a miss. Autofill the formula down to cell C101.
5. Find the overall proportion of hits, and identify the length of the longest streak of hits and the length of the longest streak of misses. Write a paragraph commenting on your proportion of hits and your "streaks."
6. Describe how the "streaks" compare for the 50 -percent and 75-percent scenarios.

Chapter 2, exercise 11

The following frequency distribution reports the number of frequent flier miles, reported in thousands, for employees of Brumley Statistical Consulting, Inc. during the first quarter of 2004.

1. How many employees were studied?

c. Construct a histogram.

Chapter 3, exercise 85

Refer to the CIA data, which reports demographic and economic information on 46 countries.

1. Select the variable Life Expectancy.

1. Find the mean, median, and the standard deviation.
2. Write a brief summary of the distribution of life expectancy.
   b. Select the variable GDP/cap.
   1. Find the mean, median, and the standard deviation.
   2. Write a brief summary of the distribution GDP/cap.

ACTIVITY 17.1

In the first part of this activity, you will generate some data that should have an approximately normal (or bell-shaped) distribution. In the second part, you will use the definition of standard deviation and compare the standard deviations for two different data sets. Work with a partner to generate the following data.

a. Toss 10 coins and record the number of heads you obtained.

b. Repeat this 24 more times until you have a list of 25 numbers, each of them between 0 and 10.

c. Retrieve the file "EA17.1 Coins and Presidents.xls" from the CD or website, and you will find the results of 35 tosses of 10 coins that someone else carried out. When you first retrieve the file, column B contains the number of times 0 heads was obtained in the 35 tosses of 10 coins, the number of times 1 head was obtained in the 35 tosses, and so on, up to the number of times 10 heads was obtained. Add your results to the list so you have a total of 60 in column B.

d. Create a scatterplot of these data, using one of the versions of the scatterplot with the dots connected. Describe what your curve looks like, including where it is "centered" and what its "spread" is.

e. Change your graph to a bar graph

f. Print your bar graph, with appropriate titles on the axes, and by hand draw in a bell-shaped curve that "fits" this data. How does your handdrawn curve compare with the curve you described in part d of this question?

Chapter 17. #20

A new machine has just been installed to cut and rough-shape large slugs. The slugs are then transferred to a precision grinder. One of the critical measurements is the outside diameter. The quality control inspector randomly selected five slugs each hour, measured the outside diameter, and recorded the results. The measurements (in millimeters) for the period 8:00 A.M. to 10:30 A.M. follow.

1. Determine the control limits for the mean and the range.
2. Plot the control limits for the mean outside diameter and the range.

Topic 17, exploration 2

The following tables provide information about the top women-owned businesses

in the U.S. The first table gives year 2000 revenue in millions of dollars

and number of employees for Pennsylvania women-owned companies with

year 2000 revenues of $70 million or higher. The second table gives the same

information for Michigan women-owned companies with year 2000 revenues

of $70 million or higher.

Pennsylvania Companies 2000 Revenue ($ million) Number of Employees

PPennsylvania Companies 2000 Revenue ($ million) Number of Employees

PA Company 2000 Revenue ($mill) # Employees

84 Lumber 2000 4400

Charming Shoppes 1600 12000

Rodale 500 1300

Mothers Work 366.3 3800

Harmelin Media 200 105

McGettigan Partners 175 400

Wetherill Associates 135 500

Hanna Holdings 73.7 1284

MI Company 2000 Revenue ($mill) # Employees

Michigan Companies 2000 Revenue ($ million) Number of Employees

Ilitch Holdings 800 700

Plastech Engineered Products 420 3500

Jerome-Duncan Ford 350 300

Elder Ford 287.6 108

Patsy Lou Williamson Auto. Gp. 221 240

Mexican Industries 174 1463

Rush Trucking 153 2000

Jaguar-Saab of Troy 143 134

Manpower Metro Detroit 118 250

Continental Plastics 107 650

Leco 82 800

Rodgers Chevrolet GEO 75 80

Strategic Staffing Solutions 75 600

Two Men & a Truck Internat’l 75 40

Systrand Manufacturing 72 230

a. Use a calculator or computer to compute the mean and standard

of the year 2000 revenue for the Pennsylvania companies in the first table.

b. Use a calculator or computer to compute the mean and standard deviation

of the year 2000 revenue for the Michigan companies in the second table.

c. Explain what the values you calculated in parts a and b of this exploration

tell you about the data sets.

d. How would the mean and standard deviations change if the largest data

value in each set were removed?

e. Find the mean and the standard deviation of the number of employees for

the Pennsylvania companies in the first table.

f. Find the mean and the standard deviation of the number of employees for

the Michigan companies in the second table and compare to your results

in part e of this exploration

Chapter 6 Emery, Finnerty, Stowe

A6. Expected portfolio return. Musumeci Capital Management has invested its portfolio as shown here. What is Musumeci's expected portfolio return?

Asset Portfolio Weight Expected Return

Money market securities 10% 4%

Corporate bonds 20 8

Equities 70 12

B6. Expected return and risk. Proctor & Gamble is considering three possible capital investment projects. The projected returns depend on the future state of the economy as given here.

a. Calculate each project's expected return, variance, and standard deviation.

b. Rank the projects on the basis of (1) expected return and (2) risk. Which project would you choose?

Projected Return

State of the Economy Probability of Occurrence 1 2 3

Recession 0.1 9% 3% 15%

Stable 0.7 13 10 11

Boom 0.2 17 22 5

B10

(Excel: Calculating means, standard deviations, covariance, and correlation). Given the probability distributions of returns for stock X and stock Y, compute:

a. The expected return for each stock

Returns

Probability Stock X Stock Y

0.2 5% 12%

0.2 10 10

0.4 12 8

0.15 14 0

0.05 18 2

Price: $44.04

Solution: The downloadable solution consists of 22 pages, 2204 words and 11 charts.
Deliverable: Word Document