# Basic Probability, Central Limit Theorem, Sampling and Indexes

Basic Probability, Central Limit Theorem, Sampling and Indexes

Basic Probability, Central Limit Theorem, Sampling and Indexes

Mary Margaret Maloney

University of Phoenix

QRB/501 – Quantitative Reasoning for Business

Professor Robert Batiste

August 3, 2009

Sevilla & Somers.

Topic 18 – Basics of Probability

Exploration 3. The following table contains information on the 2002 resident

population of the U.S., by age. (Source: The New York Times Almanac 2004,

page 277).

Age Count Cumulative Count

Younger than 18 years old 1,107,108 1,107,108

18 to 24 years old 452,196 1,559,304

25 to 44 years old 1,270,419 2,829,723

45 to 64 years old 1,068,243 3,897,966

65 years and older 588,524 4,486,508

4,486,508

- If a resident of the U.S. is chosen at random, find the probability that he or she is 25

to 44 years old.

P = 1,107,108 + 452,196 + 1,270,419 + 1,068,243 + 588,542 = 4,486,508

P = 1,270,419 / 4,486,508

P = 0.2831643 rounded to 28%

- If a resident is chosen at random, find the probability that he or she is older than 24

years old.

P = 1,107,108 + 452,196 + 1,270,419 + 1,068,243 + 588,542 = 4,486,508

P = (1,270,419 + 1,068,243 + 588,542) / 4,486,508

P = 2,927,204 / 4,486,508

P = 0.652446 rounded to 65%

Sevilla & Somers.

Topic 18 – Basics of Probability

Exploration 3. (Continued).

- In what age category does the median age fall?

There were 4,486,508 people in the survey. The median observation is:

(4,486,508 + 1) / 2= 2,243,254.5. 2,243,254.5 is the average of the 2,243,254 and

2,243,255 people surveyed. This survey is in the 25-44 year old category. This number listed in the cumulative count column. The median is in the 25 to 44 years old category.

Emery, Finnerty & Stowe

Chapter 6 – Risk and Return: Stocks

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

rp = (10 * 4) + (20 * 8) + (70 * 12)

rp = 40 + 160 + 840 = 1040 = 10.4%

Emery, Finnerty & Stowe

Chapter 6 – Risk and Returns: Stocks

B6. (Expected return and risk) Procter & Gamble is considering three possible capital

Investment projects. The projected returns depend on the future state of the

economy are given here.

B6A. Calculate each project’s expected return, variance, and standard deviation.

Project 1

rp = (.1 * 9) + (.7 * 13) + ( .2 * 17)

rp = .9 + 9.1 + 3.4 = 13.4%

Variance:

.1 * (9-13.4)² = 1.936

.7 * (13-13.4)² = .112

.2 * (17-13.4)²= 2.592

1.936 + .112 + 2.592 = 4.64

Standard Deviation: Square root of variance = 2.154065923 or 2.15

Emery, Finnerty & Stowe

Chapter 6 – Risk and Return: Stocks

B6A. (Continued).

Project 2

rp = (.1 * 3) + (.7 * 10) + (.2 * 22)

rp = .3 + 7 + 4.4 = 11.7%

Variance =

.1 * (3-11.7)² = 7.569

.7 * (10-11.7)² = 2.023

.2 * (22-11.7)² = 21.218