As was discussed in the Analytics in Action from Chapter 2, the U.S. Census Bureau is a leading source of quantitative data related to the people and economy of the United States. The crosstabulation below represents the number of households (1,000s) and the household income by the highest level of education for the head of household (U.S. Census Bureau web site, 2013). Use this crosstabulation to answer the following questions.
- a. Develop a joint
probability table. - b. What is the probability the head of one of these households has a master’s degree or higher education?
- c. What is the probability a household is headed by someone with a high school diploma earning $100,000 or more?
- d. What is the probability one of these households has an income below $25,000?
- e. What is the probability a household is headed by someone with a bachelor’s degree earning less than $25,000?
- f. Are household income and educational level independent?
a.
Create a joint probability table.
Answer to Problem 8P
The joint probability table is given below:
Highest Level of Education | Household income | |||
Under $25,000 | $25,000 to $49,999 | $49,999 to $50,000 | $100,000 and Over | |
High school graduate | 0.1505 | 0.1519 | 0.1438 | 0.0530 |
Bachelor’s degree | 0.0378 | 0.0634 | 0.1168 | 0.1191 |
Master’s degree | 0.0104 | 0.0184 | 0.0460 | 0.0624 |
Doctoral degree | 0.0012 | 0.0024 | 0.0064 | 0.0164 |
Explanation of Solution
The joint probability is calculated by dividing the intersection value of two events by the overall total.
The joint probability table is given below:
Highest Level of Education | Household income | Total | |||
Under $25,000 | $25,000 to $49,999 | $49,999 to $50,000 | $100,000 and Over | ||
High school graduate | 0.4993 | ||||
Bachelor’s degree | 0.3371 | ||||
Master’s degree | 0.1371 | ||||
Doctoral degree | 0.0265 | ||||
Total | 0.2000 | 0.2361 | 0.3130 | 0.2509 | 1 |
b.
Find the probability of the head of one of these households who has a Master’s degree or higher education.
Answer to Problem 8P
The probability the head of one of these households has a Master’s degree or higher education is 0.1636.
Explanation of Solution
The probability that the head of one of these households has a Master’s degree or higher education is calculated as follows:
Therefore, the probability that the head of one of these households has a Master’s degree or higher education is 0.1636.
c.
Find the probability that a household is headed by someone with a high school diploma earning $100,000 or more.
Answer to Problem 8P
The probability that a household is headed by someone with a high school diploma earning $100,000 or more is 0.1062.
Explanation of Solution
The probability that a household is headed by someone with a high school diploma earning $100,000 or more is calculated as follows:
Therefore, the probability that a household is headed by someone with a high school diploma earning $100,000 or more is 0.1062.
d.
Find the probability that one of the households has an income below $25,000.
Answer to Problem 8P
The probability that one of the households has an income below $25,000 is 0.2.
Explanation of Solution
The probability that one of the households has an income below $25,000 is calculated as follows:
The probability that one of the households has an income below $25,000 is 0.2.
e.
Find the probability that a household is headed by someone with a Bachelor’s degree earning less than $25,000.
Answer to Problem 8P
The probability that a household is headed by someone with a Bachelor’s degree earning less than $25,000 is 0.1122.
Explanation of Solution
The probability that a household is headed by someone with a Bachelor’s degree earning less than $25,000 is calculated as follows:
The probability that a household is headed by someone with a Bachelor’s degree earning less than $25,000 is 0.1122.
f.
Check whether the household income and educational level are independent.
Answer to Problem 8P
The household income and educational level are not independent.
Explanation of Solution
Two events are said to be independent if
From Part (c), it is obtained that
The probability of $100,000 or more is calculated as follows:
It is clear that
Want to see more full solutions like this?
Chapter 5 Solutions
Essentials of Business Analytics (MindTap Course List)
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt