A coin operated Parking Meter has the capacity to store 2001} coins. Once it is full and cannot accept any more coins in will stop working. We are particularly interested in the public parking on Elizabeth Street. The number of coins deposited daily by this meter is normally distributed with a mean of 131} and a standard deviation of\". a. Determine the probability that no more than 230 coins are deposited into the meter on a randomly selected day. [3 marks} b. M the probability that no more than 1800 coins are deposited into the meter over a period of eight days. Also briey explain why the result in part \"b" is larger than \"a". You must quote a theory in few words. [5 marks} The company has Ill] public parklng meter around the city. A random sample til 10 meters are surveyed and are l'ound to have an average age ol'36t5 days and a standard deviation of III days. c. Find 90% condence interval for the average age of all meters in the city. Be careful to state any assumptions that you need to make. Explain whether this result in consistent with the company's belief that the average age of all the phones in the city in 365 days. I Ii" marks}