The time interval between two successive customers entering a store in a mall is exponentially distributed with a mean of 6.55 seconds.
a. What is the probability that the time interval is more than 10 seconds?
b. What is the probability that the time interval is between 10 and 20 seconds?
c. On a particular day a security camera is installed. Using an entry sensor, the camera takes pictures of every customer entering the shop. It needs 0.75 second after a picture is taken to get ready for the next picture. What is the probability that the camera will miss an entering customer?
d. How quick should the camera be if the store owner wants to photograph at least 95% of entering customers?