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

$P(T > t) = \frac{36}{(6+t)^2}, \text{ } t \geq 0.$
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 5 days of emerging?



Part b)

If a large number of butterflies emerge on the same day, after how many days would you expect only 5 % to be alive?



Part c)

Calculate the mean lifetime of a butterfly after emerging from its chrysalis.