Respuesta :
Answer:
Between (253400;256600)
Step-by-step explanation:
Data given
[tex]\mu =260000[/tex] reprsent the population mean
[tex]\sigma=3300[/tex] represent the population standard deviation
The Chebyshev's Theorem states that for any dataset
- We have at least 75% of all the data within two deviations from the mean.
- We have at least 88.9% of all the data within three deviations from the mean.
- We have at least 93.8% of all the data within four deviations from the mean.
Or in general words "For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least: [tex] 1-\frac{1}{k^2}"[/tex]
So using this theorem and the part "We have at least 75% of all the data within two deviations from the mean". And using the theorem we have this:
[tex]0.75 =1-\frac{1}{k^2}[/tex]
And solving for k we have this:
[tex]\frac{1}{k^2}=0.25[/tex]
[tex]k^2 =\frac{1}{0.25}=4[/tex]
[tex]k=\pm 2[/tex]
So then we need the limits between two deviations from the mean in order to have at least 75% of the data will reside.
Lower bound:
[tex]\mu -2\sigma=260000-2(3300)=253400[/tex]
Upper bound:
[tex]\mu +2\sigma=260000+2(3300)=266600[/tex]
So the final answer would be between (253400;256600)
