Question

A meteorologist has recorded daily high temperatures for the last month, in degrees Centigrade, and he presents the mean of 21 degrees C. and standard deviation of 3 degrees C. during the evening news. While on camera, his co-anchor says that nobody understands degrees C, so he does an on-the-spot conversion of these two values to degrees Fahrenheit. What are the converted mean and standard deviation? (Note: F = (1.8)(C) + 32)

Answer 1

They would be `mu=69.8~~70F` and `sigma=5.4F`

In this case you have to use the whole conversion 'recipe' to convert `C->F` so
`muF=1.8muC+32=1.8*21+32=6 9.8~~70^0 F`
This is the linear conversion of the mean .

Since the standard deviation is a measure of deviation from the mean, we don't have to take the 32 into account, that was already done. So:
`sigmaF=1.8*sigmaC=1.8*3=5.4^0F`