Question

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

along with these areas

(a) What percentage of gasoline stations had prices within

3 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​$3.25

and $3.61?

This is the question that is presnted to us in our class what else more do you need ?

Answer 1

Hello Sir/ Mam

As per Chebyshev's inequality, for all distributions with finite variance, the proportion of observations within "k" standard deviations of arithmetic mean is at least (1 - 1/k²) when k > 1.

Hence, given, mean = $3.43, standard deviation = $0.09

(a) For k = 3,

(b) For k = 2.5

Prices that are in range of 2.5 standard deviation of the mean :

($3.43 - 2.5*0.09 , $3.43 + 2.5*0.09) = ($3.205 , $3.655)

(c)

The same can also be computed using upper limit.

Hence, percentage of gasoline stations that had prices between $3.25 and $3.61 are at least :

I hope this solves your doubt.

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