In 1950 an experiment was done observing the time gaps between successive cars on the Arroyo Seco Freeway. The data show that the density function of these time gaps was given approximately by $p(t) = a e^{-0.12 t}$ where $t$ is the time in seconds and $a$ is a constant.

1. Find the constant $a$.
   $a =$
   
   
2. Find the cumulative distribution function $P(t)$. You should also sketch a rough graph of density function $p(t)$ and the cumulative distribution function $P(t)$.
   $P(t) =$
   
   
3. Find the mean and median time gap.
   Mean =
   Median =