Question

Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.96 with a standard deviation of $0.12. Using Chebyshev's Theorem, what is the minimum percentage of stores that sell a gallon of milk for between $3.72 and $4.20? Round your answer to one decimal place.

Answer 1

1-(1/2^2)=1-(1/4)=(3/4)=.75=75%

Answer 2

25%

Explanation:

Given that prices of a gallon of milk at various stores in one town have a mean of $3.96 with a standard deviation of $0.12.

When sales lie between 3.72 and 4.20 dollars we get

we have 3.72 = 3.96-2 (0.12) and

4.20 = 3.96+2(0.12)

Hence simply we can write

`P(|x-Mean|<2 \sigma) \geq (1)/(4) \\=0.25`

i.e. 25% is the minimum percentage of stores that sell a gallon of milk for between $3.72 and $4.20