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 themean?

(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/k^{2})
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.

Do give a thumbs up if you find this helpful.

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