Price of electricity The Energy Information Administration r

Price of electricity: The Energy Information Administration records the price of electricity in the United State each month. In July 2013, the average price of electricity was 11.92 cents per kilowatt-hour. Suppose that the standard deviation is 2.1 cents per kilowatt-hour. What can you determine about these data by using Chebyshev\'s Inequality with K=3?

Solution

The energy information administration records the price of electricity in the United States each month.

Average price (mu) = 11.92 cents

standard deviation (sd) = 2.1 cents

Chebyshev\'s inequality guarantees that in any probability distribution, \"nearly all\" values are close to the mean — the precise statement being that no more than 1/k² of the distribution\'s values can be more than k standard deviations away from the mean (or equivalently, at least 11/k² of the distribution\'s values are within k standard deviations of the mean).

Here we are given that k=3,

1 - 1/k² = 1 - 1/3² = 88.9%

  That is 88.9% of the values are lie within 3 standard deviation of the mean.

lower limit = mu - 3*sd = 11.92 - 3(2.1) = 5.62

upper limit = mu + 3*sd = 11.92 + 3(2.1) = 18.22

That is 88.9% of the data values are lie within 5.62 and 18.62.