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A company operates a solar installation in the desert in Western Australia. It is reviewing its...

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Basic Math

A company operates a solar installation in the desert in WesternAustralia. It is reviewing its operating practices with a view tomaking them more efficient. The solar installation generateselectric power from sunlight and incurs operating costs forcleaning the solar modules (sometimes called solar panels) andreplacing solar modules that have failed.

a) The annual revenue from the electric power is variable due tovariable cloudiness and solar module failure and has a mean of$2.78m and a standard deviation of $0.32m. The annual operatingcosts have a mean of $0.51m and a standard deviation of $0.12m.Expected revenue varies systematically from one month to another,being higher in the summer when there is more sunshine. Monthlyoperating costs follow the same probability model regardless of themonth (same mean and standard deviation apply to all months).Calculate, if possible, the mean and standard deviation of (i)monthly operating costs (ii) monthly profits. If a calculation isnot possible, give the reason.

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