(Solved): please answer both if possible thanks! Dinner customers at the Red Iguana Restautant often experienc ...

Dinner customers at the Red Iguana Restautant often experience a long wait for a table. For a randomly selected customer who amives at the restamrant between 6:00 PM and 7.00 PM, the waiting time (in minutes) is a continuous random variable such that \[ f(x)=\left\{\begin{array}{ll} 0.05 e^{-0.05 x}, & x \geq 0 \\ 0, & \text { otherwise } \end{array}\right. \] (a) Suppose a dinner customer is randomly selected. What is the probability that the person must wait for a table at most 20 minutes? Show correct probability notation. (4 pts) (b) Suppose a dinner customer is randomly selected. What is the probability that the person must wait for a table between 15 and 30 minutes? Show correct probability notation. ( 4 pts)