Chapter 6, Problem 57RE

Psychology. Rats were trained to go through a maze by rewarding them with a food pellet upon successful completion of the run. After the seventh successful run. the probability density function for length of time (in minutes) until success on the eighth trial was given by

$f\left(t\right)=\{\begin{array}{cc}.5e^{-.5t}& \text{if}t\ge 0\\ 0& \text{otherwise}\end{array}$

What is the probability that a rat selected at random after seven successful runs will take 2 or more minutes to complete the eighth run successfully? [Recall that the area under a probability density function curve from −∞ to ∞ is 1.]