Problem 2 (10 marks) The time taken to manually wash a car at a car wash can be modelled as an exponential distribution with a mean of 20 minutes. (a.) (2 marks) What is the probability that the car gets washed within 15 minutes? [Hint: the formula for computing integrals of the form f: TineElmd'\" is given on Page 4 in the formula sheet]. (b.} (3 marks} The car washing center pays out a small bonus if an employee washes a car in 15 minutes or less. Suppose an employee washes 5 cars before lunch. What is the probability that at least 2 of these will result in bonus payments? Carefully state your assumptions. (c.) (2 marks) lCl'ut of the 5 cars washed by the employee in (b.} what is the probability that exactly one results in a bonus payment? (d.} (3 marks} Suppose the employer pays out a larger bonus if 4 cars are each washed in 15 minutes or less during a day. What is the probability that an employee receives the larger bonus payment when the 13th car of the day is washed