Question

At one point the average price of regular unleaded gasoline was ?$3.57 per gallon. Assume that the standard deviation price per gallon is ?$0.07 per gallon and use? Chebyshev's inequality to answer the following.

?(a) What percentage of gasoline stations had prices within 4 standard deviations of the? mean? ?

(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the? mean? What are the gasoline prices that are within 2.5 standard deviations of the? mean? ?

(c) What is the minimum percentage of gasoline stations that had prices between ?$3.43 and ?$3.71??

Answer 1

a) According to Chebyshev's inequality ,

K is the number of standard deviation away from the mean.

For, the percentage of gasoline stations had prices within 4 standard deviations of the? mean

is  

K =4

Answer: The percentage of gasoline stations had prices within 4 standard deviations of the? mean is 93.75%

b) K = 2.5

Answer: The percentage of gasoline stations had prices within 2.5 standard deviations of the? mean is 84%

The gasoline prices  that are within 2.5 standard deviations of the? mean is

   to

= 3.57- 2.5*0.07 to 3.57+2.5*007

Answer: = $3.395 to $3.745

c) $3.43 and $3.71

Proportion is

Answer: Atleast 75%