Question

From a sample with nequals24​, the mean number of televisions per household is 4 with a standard deviation of 1 television. Using​ Chebychev's Theorem, determine at least how many of the households have between 2 and 6 televisions. At least nothing of the households have between 2 and 6 televisions.

Answer 1

At least 18 of the households have between 2 and 6 televisions.

Explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by
`100(1 - (1)/(k^(2)))`.

In this question:

Mean = 4

Standard deviation = 1

Percentage of households that have between 2 and 6 televisions.

2 = 4 - 2*1

So 2 is two standard deviations below the mean

6 = 4 + 2*1

So 6 is two standard deviations above the mean

By Chebyshev's Theorem, at least 75% of the measures are within 2 standard deviations of the mean.

Out of 24

0.75*24 = 18

At least 18 of the households have between 2 and 6 televisions.