Answer:
Atleast, 88.9% of the households have between 2 and 6 televisions.
Step-by-step explanation:
We are given the following in he question:
Sample size, n = 32
Mean, μ = 4
Standard Deviation, σ = 1
Chebychev's Theorem:
- I states that atleast
percent of data lies within k standard deviations for a non normal data. - For k = 2
![1-\dfrac{1}{2^2} = 0.75](https://tex.z-dn.net/?f=1-%5Cdfrac%7B1%7D%7B2%5E2%7D%20%3D%200.75)
Atleast 75% of data lies within 2 standard deviation of mean.
![1-\dfrac{1}{3^2} = 0.889](https://tex.z-dn.net/?f=1-%5Cdfrac%7B1%7D%7B3%5E2%7D%20%3D%200.889)
Atleast 88.9% of data lies within 3 standard deviation of mean.
![2 = \mu - 2\sigma = 4 - 2(1)\\6 = \mu + 2\sigma = 4 +2(1)](https://tex.z-dn.net/?f=2%20%3D%20%5Cmu%20-%202%5Csigma%20%3D%204%20-%202%281%29%5C%5C6%20%3D%20%5Cmu%20%2B%202%5Csigma%20%3D%204%20%2B2%281%29)
Thus, we have to find data within two standard deviations.
Atleast, 88.9% of the households have between 2 and 6 televisions.