# Getting the variance of a data set when only given the mean and variance of a related data set.

Call x the atmospheric carbon dioxide level in parts per million by volume. Call y the change in the earth’s surface temperature over the next 50 years, in degrees celsius. Suppose that climate scientists estimate this relationship:

y = 0.20 · (x − 390).

Suppose x has a mean of 410 and a variance of 18. Find the mean and variance of the change in the temperature.

I have already solved for the mean of the temperature, it came out to be 4 but from there I am unsure of how to go about taking the data given and finding the variance of the temperature.

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