SOLUTION: Hello! Can someone please help me solve this problem: A random sample of 50 gas stations in cook County, Illinois, result in a mean price per gallon of $1.60 and a standard devi

Question 484125: Hello! Can someone please help me solve this problem:
A random sample of 50 gas stations in cook County, Illinois, result in a mean price per gallon of $1.60 and a standard deviation of $0.07.
a) determine the percentage of gas stations that have prices between $1.46 and $1.74, according to the Empirical Rule.
b) Determine the percentage of gas stations that have prices between $1.46 and $1.74, according to the Chebyshev's theorem.
Thank you!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A random sample of 50 gas stations in cook County, Illinois, result in a mean price per gallon of $1.60 and a standard deviation of $0.07.
a) determine the percentage of gas stations that have prices between $1.46 and $1.74, according to the Empirical Rule.
---
1.46-1.60 = -0.14 = -2*0.07 or 2 standard deviations below the mean.
----
1.74-1.60 = +0.14 = +2*0.07 or 2 standard deviations above the mean.
----
P(1.46 < x < 1.74) = P(-2 < z < 2) = 0.9545 = 95.45%
========================================================
b) Determine the percentage of gas stations that have prices between $1.46 and $1.74, according to the Chebyshev's theorem.
---
Percentage within 2 standard deviations of the mean
= (1-(1/2)^2) = 0.75 = 75%
============================
Cheers,
Stan H.

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