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

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In summary, the conversation discusses the interest of BIG Corporation in the lifetimes of its Ultra batteries and the use of Chebyshev's Theorem and the empirical rule to determine the distribution of these lifetimes. The mean lifetime of the Ultra batteries is stated to be ___ hours, with a standard deviation of ___ hours. Based on this information, the conversation poses questions about the percentage of lifetimes that lie between certain values according to Chebyshev's Theorem and the empirical rule. However, the parameters of the distribution (mean and standard deviation) must be known in order to solve these questions.
  • #1
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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  • #2
You need to know the parameters ([itex]\mu, \sigma[/itex]) in terms of hours.
 
  • #3
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.
 

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

What is Chebyshev's Theorem?

Chebyshev's Theorem, also known as Chebyshev's Inequality, is a statistical theorem that provides a measure of how much data is expected to deviate from its mean. It is a useful tool for understanding the spread of data in a distribution.

How is Chebyshev's Theorem used?

Chebyshev's Theorem is used to find the proportion of data that falls within a certain number of standard deviations from the mean. This can help identify outliers and understand the spread of data in a distribution.

What are the assumptions of Chebyshev's Theorem?

Chebyshev's Theorem assumes that the data is normally distributed and that the mean and standard deviation are known or can be estimated.

What is the relationship between Chebyshev's Theorem and the Empirical Rule?

Chebyshev's Theorem is a more general version of the Empirical Rule, which only applies to data that is normally distributed. Chebyshev's Theorem applies to any type of distribution and provides a more conservative estimate of the proportion of data within a certain number of standard deviations from the mean.

How is Chebyshev's Theorem different from the Central Limit Theorem?

Chebyshev's Theorem is a general theorem that applies to any type of distribution, while the Central Limit Theorem only applies to normally distributed data. Additionally, Chebyshev's Theorem provides a measure of how much data is expected to deviate from the mean, while the Central Limit Theorem focuses on the behavior of sample means as sample size increases.

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