The time that a butterfly lives after emerging from its chrysalis can be modelled by a continuous random variable t in days whose probability density function is given by 72 f t 6 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 4 days of emerging Part b If a large number of butterflies emerge on the same day after how many days would you expect only 4 to be alive Part c Calculate the mean lifetime of a butterfly after emerging from its chrysalis