Question
Asked Oct 8, 2019

I'm having an issue with applying emperitical and cherbov therom to the word problems. i understand how to plug the numbers in but when it asks for the percentage between the numbers i dont understand

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Step 1

The 68-95-99.7% (Empirical) Rule:

For a normal distribution, the empirical rule (68-95-99.7% Rule) state that 68% of the observations falls within 1 standard deviation of mean, 95% of the observations falls within 2 standard deviations of mean, and 99.7% of the observations falls within 3 standard deviations of mean respectively.

 

If a population has bell shaped distribution with mean µ and standard deviation σ ;

  • Approximately 68% of the observations lie between µ – σ and µ + σ.
  • Approximately 95% of the observations lie between µ – 2σ and µ + 2σ.
  • Approximately all of the observations lie between µ – 3σ and µ + 3σ.
Step 2

For example:

Consider the weight of freshmen follows normal distribution with mean of 160 and standard deviation of 11. The sample size n is 300.

The interval for 2 standard deviations of the mean is obtained as follows:

20 160 2(11)
=(160 22,160+22)
-(138,182)
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20 160 2(11) =(160 22,160+22) -(138,182)

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Step 3

Chebyshev’s inequality:

Chebyshev’s rule is appropriate for any distribution. That is, Chebyshev’s inequality applies to all distributions, regardless of shape. Moreover, it provides the minimum percentage of the observation that lies within k standard deviations of the mean.

  • It is possible that very few measurements will fall within one standard deviation of the mean.
  • If k = 2, at least 3/4 of...

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