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, please 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?