The time that a butterfly lives after emerging from its chrysalis can be modelled by a random variable t, the model here taking the probability that a butterfly survives for more than t days as p(t> t)=36(6+t)2, t≥0. for these problems, ensure your answers are accurate to within 3 decimals. part a) what is the probability that a butterfly will die within 6 days of emerging? 0.75 part b) if a large number of butterflies emerge on the same day, after how many days would you expect only 6 % to be alive? 18.494 part c) calculate the mean lifetime of a butterfly after emerging from its chrysalis?