(a)
The number of times the light is red is a binomial random variable.
(a)
Answer to Problem 84E
Since all four conditions have been satisfied, Y is a binomial random variable.
Explanation of Solution
Given information:
Number of trials,
Y : The number of times that the light is red.
For the binomial random variable,
The four conditions are as follows:
Binary: Since the success resembles the light is red and failure resembles the light is not is not red. Thus, the condition is satisfied.
Independent trials: It is known that Pedro’s working days are chosen at random. Thus, the condition has been satisfied.
Fixed number of trials: Since we chose 10 Pedro’s work days. Thus, the number of trials is 10 and the condition has been satisfied.
Probability of success: Since there are 55% chances for the light to be red. Thus, the probability for the light to be red is 55% and the condition has been satisfied.
Hence,
All the conditions are satisfied.
According to this scenario,
Y describes a binomial setting.
(b)
Probability for the light is red on exactly 7 days.
(b)
Answer to Problem 84E
The probability that the light is red on exactly 7 days is approx. 0.1665.
Explanation of Solution
Given information:
Number of trials,
Probability of success,
According to the binomial probability,
At
The binomial probability to be evaluated as:
Thus,
Around 16.65% chances are there for the light to be red on exactly 7 days and the probability is approx. 0.1665.
Chapter 6 Solutions
PRACTICE OF STATISTICS F/AP EXAM
Additional Math Textbook Solutions
Introductory Statistics (10th Edition)
Elementary Statistics
Elementary Statistics: Picturing the World (6th Edition)
Statistics for Psychology
STATS:DATA+MODELS-W/DVD
Intro Stats, Books a la Carte Edition (5th Edition)
- 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