Anonymous
Anonymous asked in EnvironmentGreen Living · 3 months ago

Solar energy is considered by many to be the energy of the future. A recent survey was taken to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of \$98 and a standard deviation of \$14. If the distribution is normal, what percentage of homes will have a monthly utility bill of more than \$84?

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• Please note:  The percentages stated below are based on your question using two significant digits.  The actual percentages have an infinite number of decimal places, but round to the values mentioned.

In a "Normal" distribution curve, 50% of values fall above the mean and 50% fall below it.  68% of values fall within one standard deviation (both + and -) of the mean.  Which means that 34% fall between the mean and one standard deviation below it.

Given the mean of \$98 and standard deviation of \$14, that means that \$84 is one SD below the mean.

Add the two ranges together, and you get:

50% above \$98 (mean)

34% between \$98 and \$84 (one SD below)

So 84% of the values are above \$84.

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Alternatively, you can say that 68% are within one SD, and the rest (32%) are outside it.  16% above and 16% below.

Since 16% are below \$84, the rest (100-16=84%) are above it.

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• It's either 16, 32, 84, 95. Don't remember how to actually compute it. I tried four different ways and these are the answers I came up with. I know three of them are wrong and one is right but don't know which are which.

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