At one point the average price of regular unleaded gasoline was $3.52 per gallon. Assume that the standard deviation price per gallon is $0.06 per gallon and use Chebyshev�s inequality to answer the following.

a. At least % of gasoline stations had prices within 4 standard deviations of the mean. (round to the nearest hundredth as needed)
b. At least % of gasoline stations had prices within 1.5 standard deviations of the mean.
c. The gasoline prices that are within 1.5 standard deviations of the mean are $ to $ (Use ascending order)
d. % is the minimum percentage of gasoline stations that had prices between $3.40 and $3.64. (round to the nearest hundredth as needed)

a)  

At least 93.75% of gasoline stations had prices within 4 standard deviations of the mean. (round to the nearest hundredth as needed)

b)  

At least 55.56% of gasoline stations had prices within 1.5 standard deviations of the mean. (round to the nearest hundredth as needed)

c)

d)

And since we have the value of k we have:

75% is the minimum percentage of gasoline stations that had prices between $3.40 and $3.64. (round to the nearest hundredth as needed)

Step-by-step explanation:

Data given  

reprsent the sample mean

represent the sample standard deviation

The Chebyshev's Theorem states that for any dataset

•We have at least 75% of all the data within two deviations from the mean.

•We have at least 88.9% of all the data within three deviations from the mean.

•We have at least 93.8% of all the data within four deviations from the mean.

Or in general words "For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least:

Part a

At least 93.75% of gasoline stations had prices within 4 standard deviations of the mean. (round to the nearest hundredth as needed)

Part b

At least 55.56% of gasoline stations had prices within 1.5 standard deviations of the mean. (round to the nearest hundredth as needed)

Part c

For this case we have:

Part d

For this case we can find the number of k like this:

And since we have the value of k we have:

75% is the minimum percentage of gasoline stations that had prices between $3.40 and $3.64. (round to the nearest hundredth as needed)

combine all like terms then its just a 2 step equation