37.3k views
4 votes
From a sample with n=20​, the mean number of televisions per household is 2 with a standard deviation of 1 television. Using​ Chebychev's Theorem, determine at least how many of the households have between 0 and 4 televisions. At least nothing of the households have between 0 and 4 televisions.

User Dseibert
by
8.9k points

1 Answer

4 votes

Answer:

At least 15 households have between 0 and 4 televisions.

Explanation:

Chebychev's Theorem:

P(|X-μ|>kσ)≤
(1)/(k^2)

μ= mean

σ= standard deviation

k= number of typical deviations

It is also expressed as:

P(μ-kσ<X<μ+kσ)≥
1-(1)/(k^2)

Using​ Chebychev's Theorem, we determine:

P(0<X<4)

μ-kσ=0 ⇒ 2-k·1=0 ⇒k=2

μ+kσ=4 ⇒ 2+k·1=4 ⇒k=2

P(0<X<4)=
1-(1)/(2^2)=0.75

For a sample n=20,

0.75×20=15

At least 15 households have between 0 and 4 televisions.

User Scz
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories