Concept explainers
a.
Check whether the random variable is discrete or continuous.
a.
Answer to Problem 128UP
The variable “The length of time that an exercise physiologist’s program takes to elevate her client’s heart rate to 140 beats per minute” is continuous.
Explanation of Solution
The random variable is “The length of time that an exercise physiologist’s program takes to elevate her client’s heart rate to 140 beats per minute”.
Discrete variable: It is a quantitative variable. It consists of either a finite number of possible values or countable number of possible values. Discrete variable cannot take every possible value between two possible values.
Continuous variable: It is a quantitative variable. It consists of an infinite number of possible values that are not countable. Countable variable can take every possible values between any two possible values.
One can measure the length of time that an exercise physiologist’s program takes to elevate her client’s heart rate to 140 beats per minute but cannot count the length of time that an exercise physiologist’s program takes to elevate her client’s heart rate to 140 beats per minute. Therefore, here, one can take every admissible value between two possible values.
Thus, the length of time that an exercise physiologist’s program takes to elevate her client’s heart rate to 140 beats per minute is a continuous random variable.
b.
Explain whether the random variable is discrete or continuous.
b.
Answer to Problem 128UP
The variable “The number of crimes committed on a college campus per year” is discrete.
Explanation of Solution
The random variable is “The number of crimes committed on a college campus per year”.
One can count the number of crimes committed on a college campus per year and which is a whole number like 0, 1, 2, and so on. Thus, the number of crimes committed on a college campus per year is a finite value; it cannot be any value between two possible values.
Thus, the number of crimes committed on a college campus per year is a discrete random variable.
c.
State whether the random variable is discrete or continuous.
c.
Answer to Problem 128UP
The variable “The number of square feet of vacant office space in a large city” is continuous.
Explanation of Solution
The random variable is “The number of square feet of vacant office space in a large city”.
One can measure the square feet of vacant office space in a large city but cannot count the square feet. Therefore, here, one can take any admissible value between two possible values.
Thus, the number of square feet of vacant office space in a large city is a continuous random variable.
d.
State whether the random variable is discrete or continuous.
d.
Answer to Problem 128UP
The variable “The number of voters who favor a new tax proposal” is discrete.
Explanation of Solution
The random variable is “The number of voters who favor a new tax proposal”.
One can count the number of voters who favor a new tax proposal and which is a whole number such as 0, 1, 2, and so on. Thus, the number of voters who favor a new tax proposal is a finite value; it cannot be any possible value between two possible values.
Thus, the number of voters who favor a new tax proposal is a discrete random variable.
Want to see more full solutions like this?
Chapter 4 Solutions
Statistics 13th.ed. Instructor's Copy
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman