The snowy tree cricket, Decanthus fuftcnr', has an interesting characteristic in that the number of chirps it makes in a specific time interval can be used to accurately predict the temperature it is situated in. Let the random variable X represent the number of chirps a snowy tree cricket makes; in an eight second interval. The distribution of X is given by: x 12 15 13 21 24 at) 0.11 0.23 0.39 {115 0.12 {a} [2 marks] Find the variance in the number of chirps the snowy tree cricket makes in an eight second interval. (b) A natural phenomenon called Dolbear's Law says that you can accurately predict the temperature by counting the number of chirps the snowy tree cricket makes in an eight second interval and then add 5 to find the temperature (given in degrees Celsius). That is, the temperature can be found by calculating X + 5. Using your answer to part (a), find the standard deviation in the temperature. In other words, find the standard deviation of X + 5, which is ox+5 . (Hint: There is a very short way to do this. Look at the variance and standard deviation rules we saw in Set 10.)