Question

MTH 265-01 SP 2019 Thomas Vance& 1/23/19 11:13 AM omework: Homework 4 Save HW Score: 33.33%, 8 of 24 pts core: 0 of 1 pt 2.4.35 From a sample with m- 28, the mean number of televisions per household is 3 with a standard deviation of 1 television Using Chebychev's Theorem, determine at least how many of the households have between 1 10 of 24 (8 complete) Question Help and 5 televisions Simplity your answer.) Enter your answer in the answer box and then click Check Answer Clear Al All parts showing

Answer 1

According to Chebyshev's the percentage of data that lies within 'K' Standard deviation is at least

$1-\frac{1}{K^{2}}$

here in the data given where mean =3 and K=1 hence, X=1 lies at -2 standard deviations and X=5 lies at 2 standard deviations so,

$1-\frac{1}{2^{2}}=0.75\Leftrightarrow 75 percent$

So if n=28 then within{1,5} minimum of 0.75* 28=21

At least 21 Households have 1 to 5 televisions.