The price of gasoline was ​$3.43 per gallon at one point. Assume that the standard deviation price per gallon is ​$0.09 per gallon and use​ Chebyshev's inequality to answer the following.

Question

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

​(b) What 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 ​$3.16 and ​$3.70​?

Answer 1

(a) 95% of the data is within 2 standard deviations of the mean

(b) Per Chebyshev, 1 - 1/k^2 = 1 - 1/(1.5)^2 = 1 - 1/2.25 = 1 - reciprocal(9/4) = 1 - 4/9 = 5/9

regardless of the distribution.

so 55 and 5/9 % of the data lies within 1/5 standard deviation of the mean

We cannot calculate probabilities without the mean AND assuming the gas prices are

normally distributed.

$3.43 was a price, but WAS IT THE MEAN????

Please repost