2017 September 30,
Carleton College, Prof. Joshua R. Davis
Complete these problems. Write them up carefully, in the order assigned, for handing in with the rest of your homework.
An entrepreneur is considering whether to build a motel in a certain location near a highway. Her research suggests that an average of 35 car-loads of people seek accommodation near that location each day. She assumes that each car-load will occupy one room for one night. How many rooms should the motel have, so that it is full 95% of the nights?
An engineer is developing a device that is intended to work probabilistically with probability 70%. That is, the device will solve its problem 70% of the time and fail to solve the problem 30% of the time. (Many powerful algorithms in computer science are probabilistic like this, such as the Miller-Rabin primality test.) However, during the design phase of the project, the engineer was only 85% sure that her design was correct. And now, in the testing phase, the device has failed its first 3 tests. Based on this testing and her original confidence, what is the probability that the device is working correctly? Answer using the geometric distribution, conditioning on whether the device was designed correctly.