What percentage of Ultra battery lifetimes fall between 719 and 1059 hours?

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SUMMARY

The discussion focuses on determining the percentage of Ultra battery lifetimes that fall between 719 and 1059 hours using Chebyshev's Theorem and the empirical rule. Participants emphasize the necessity of knowing the mean and standard deviation of the battery lifetimes to apply these statistical methods effectively. Without these parameters, it is impossible to accurately calculate the required percentages. The conversation highlights the importance of statistical foundations in analyzing battery performance data.

PREREQUISITES
  • Understanding of Chebyshev's Theorem
  • Familiarity with the empirical rule in statistics
  • Knowledge of mean and standard deviation concepts
  • Basic statistical analysis skills
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  • Research how to calculate mean and standard deviation for a dataset
  • Learn about Chebyshev's Theorem applications in real-world scenarios
  • Study the empirical rule and its implications for normally distributed data
  • Explore statistical software tools for data analysis, such as R or Python's NumPy library
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Statisticians, data analysts, and product developers interested in battery performance metrics and statistical analysis techniques.

lost007
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I know what the theorem states, but can't figure out how to input the data to make it work. Example

BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries, hoping to obtain its share of a market boosted by the popularity of portable CD and MP3 players. To investigate its new line of Ultra batteries, BIG randomly selects Ultra batteries and finds that they have a mean lifetime of hours, with a standard deviation of hours. Suppose that this mean and standard deviation apply to the population of all Ultra batteries. Complete the following statements about the distribution of lifetimes of all Ultra batteries.


According to Chebyshev's Theorem, at least 36% of the lifetimes lie between ___hrs & ___hrs

According to Chebyshev's Theorem, at least ?% of the lifetimes lie between 719hrs & 1059hrs

According to the empirical rule, Suppose the distribution is bell-shaped, approximately what % of the life-times lie between 719 hours & 1059 hrs?

Suppose the distribution is bell-shaped. According to the empirical rule, approximately 68% of the lifetimes lie between ___hours & ____hrs?
 
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You need to know the parameters ([itex]\mu, \sigma[/itex]) in terms of hours.
 
yes, to clarify, you need to provide us first with the given MEAN and the given STANDARD DEVIATION before we can even begin to answer this problem. If you are not given that I do not know if you can solve this problem.
 

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