Respuesta :
Answer: There are atleast 15 households that have between 2 and 6 televisions.
Step-by-step explanation:
Since we have given that
n = 20
mean number of televisions per household = 4
Standard deviation = 1
we need to find the number of the households have between 2 and 6 television.
First we check the within numbers.
[tex]\mu-x_1=4-2=2\\\\x_2-\mu=6-4=2[/tex]
so, we can say that there are 2 television which is within numbers.
So, now, we will find the value of k:
[tex]k=\dfrac{\text{within number}}{\text{Standard deviation}}\\\\k=\dfarc{2}{1}=2[/tex]
Using the Chebychev's theorem, we get that
[tex]1-\dfrac{1}{k}^2\\\\=1-\dfrac{1}{2^2}\\\\=1-\dfrac{1}{4}\\\\=\dfrac{4-1}{4}\\\\=\dfrac{3}{4}[/tex]
so, the number of the households would be
[tex]\dfrac{3}{4}\times 20\\\\=3\times 5\\\\=15[/tex]
Hence, there are atleast 15 households that have between 2 and 6 televisions.
There are at least 15 households that have between 2 and 6 televisions and this can be determined by using Chebychev's Theorem.
Given :
From a sample with n equals 20, the mean number of televisions per household is 4 with a standard deviation of 1 television.
In order to determine the number of households that have between 2 and 6 televisions, first check:
[tex]\mu-x_1=4-2 = 2[/tex]
[tex]x_2-\mu = 6-4 = 2[/tex]
So, from the above calculation, it can be said that there are 2 television which is within the numbers.
Now, the value of k is given by the formula:
[tex]\rm k =\dfrac{Within\; Number}{Standard\; Deviation}[/tex]
k = 2
Now, using Chebychev's Theorem.
[tex]\rm =1-\left(\dfrac{1}{k}\right)^2[/tex]
[tex]\rm =1-\left(\dfrac{1}{2}\right)^2[/tex]
[tex]=\dfrac{3}{4}[/tex]
So, the total number of households is:
[tex]=\dfrac{3}{4}\times 20[/tex]
= 15
Therefore, there are at least 15 households that have between 2 and 6 televisions.
For more information, refer to the link given below:
https://brainly.com/question/23017717
