A biostatistician is investigating the time t to death of a

Question

A biostatistician is investigating the time, T, to death of a mouse exposed to a newly developed pesticide. He finds that the pdf of T is given by the following formula  f(t) = 15t²e^-5t3. Which of the following statements best describes the value of the pdf evaluated at t = .5, that is, f(.5)? Justify your answer.

1. f(.5) is the median time to death.
2. f(.5) is the rate of change in the cdf, F(t) at time t = .5
3.  50% of all mice exposed to the pesticide will die before time f(.5).
4. f(.5)% of all mice exposed to the pesticide will die.