52,704 views
32 votes
32 votes
from a sample with n=8, the mean number of televisions per household is 2 with a standard deviation of 1 television. using chebychevs theorem, determine at least how many households have between 0 and 4 televisions

User Ndrix
by
2.6k points

1 Answer

25 votes
25 votes

n=8

Mean number of televesions per household= 4

Standard deviation= 1

Find the number of households have between 0 and 4 television

As a first step we are going to check the within numbers:


\begin{gathered} \mu=\operatorname{mean} \\ \mu-x_1=4-0=4 \\ x_2-\mu=4-4=0 \end{gathered}

So, now, we can find the value of k:


\begin{gathered} k=\frac{\text{within number}}{\text{standard deviation}} \\ k=(4)/(1)=4 \end{gathered}

Now, using the chebychev's theorem:


1-(\frac{1^{}}{k})^2\text{ }
1-(1)/(16)=(15)/(16)

Then, the number of the house holds would be:


(15)/(16)\cdot8=(15)/(2)=7.5

There are at least 7.5 households that have between 0 and 4 televisions

User VishalPandita
by
2.7k points