Answer to Question #279796 in Statistics and Probability for amanda

Question

In December​ 2018, the average price of regular unleaded gasoline excluding taxes in the United States was ​$3.06 per gallon. Assume that the standard deviation price per gallon is ​$0.11 per gallon and use​ Chebyshev's Inequality to answer the following.

​(a) What minimum percentage of gasoline stations had prices within 2 standard deviations of the​ mean?

​(b) What minimum percentage of gasoline stations had prices within 1.5 standard deviations of the​ mean? What are the gasoline prices that are within 1.5 standard deviations of the​ mean?

​(c) What is the minimum percentage of gasoline stations that had prices between ​$2.62 and ​$3.50​?

​(a) At least

enter your response here

​% of gasoline stations had prices within 2 standard deviations of the mean.

​(Round to two decimal places as​ needed.)

Answer 1

By Chebyshev's Theorem, the minimum percentage of measures within k standard deviations of the mean is:

a)

$k=2$

$P=100(1-1/2^2)=75\%$

b)

$k=1.5$

$P=100(1-1/1.5^2)=55.56\%$

gasoline prices that are within 1.5 standard deviations of the​ mean:

min: $3.06-1.5\cdot0.11=2.895$

max: $3.06+1.5\cdot0.11=3.225$

c)

$k=4$

$P=100(1-1/4^2)=93.75\%$