Concept explainers
To Calculate: The probability that the random variable in a
Answer to Problem 17E
For any normal distribution, the probability that the random variable lies within two standard deviations of the mean is
Explanation of Solution
Given Information: The random variable is normally distributed and the interval for which probability is to be calculated is from
Concept Used: The required probability is same for any normal distribution, that is, the probability is the same for any pair of values of
Calculation: Since the probability is the same for any value of mean and standard deviation, replace
For example, put
Now the probability is given by
Since the above integral contains
Therefore, for any normal distribution, the probability that the random variable lies within two standard deviations of the mean is
Chapter 6 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning