Concept explainers
Chebyshev’s theorem states that for any set of numbers, the fraction that will lie within k standard deviations of the mean (for k > 1) is at least
For example, at least 1 − 1/22 = 3/4 of any set of numbers lie within 2 standard deviations of the mean. Similarly, for any probability distribution, the probability that a number will lie within k standard deviations of the mean is at least 1 − 1/k2. For example, if the mean is 100 and the standard deviation is 10, the probability that a number will lie within 2 standard deviations of 100, or between 80 and 120, is at least 3/4. Use Chebyshev’s theorem to find the fraction of all the numbers of a data set that must lie within the following numbers of standard deviations from the mean.
13. 3
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Finite Mathematics and Calculus with Applications (10th Edition)
- A manufacturer has determined that a machine averages one faulty unit for every 500 it produces. What is the probability that an order of 300 units will have one or more faulty units?arrow_forwardIf a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning