Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.74 with a standard deviation of $0.09. Using Chebyshev's Theorem, what is the minimum percentage of stores that sell a gallon of milk for between $3.56 and $3.92? Round your answer to one decimal place.

Respuesta :

Note that $3.56 is 2 standard deviations below the mean, and $3.92 is 2 standard deviations above the mean.

Chebyshev's theorem says that

[tex]P(|X-\mu|\le k\sigma)\ge1-\dfrac1{k^2}[/tex]

In this case we take [tex]k=2[/tex], and we're given [tex]\mu=\$3.74[/tex] and [tex]\sigma=\$0.09[/tex], so

[tex]P(\$3.56<X<\$3.92)\ge1-\dfrac14=0.75[/tex]

making the minimum percentage 75%.