SECTION A (50 marks) Answer ALL questions in this section. QUESTION A1 [5 marks! Self-driving and parking cars use deep learning, to recognize the space around a vehicle. Technology company Nvidia uses AI to give cars the power to see, think, and learn, so they can navigate a nearly innite range of possible driving scenarios. The company's AI-powered technology is already in use in cars made by Toyota, Mercedes-Benz, Audi, Volvo, and Tesla, and is sure to revolutionize how people drive and enable vehicles to drive themselves. However, during the rst stage development, the system made a 2% inaccurate move (i.e. accident in the parking lot). They made a trial of 6,000 times to see the effectiveness. Find the probability that in the trial of 6,000 times, the system moves less than 100 inaccurate moves. QUESTION A2 15 marks} Making mistakes on your tax return can cost you money. You may miss out on a larger refund than you claimed, wind up owing more taxes, plus interest and penalties, or invite an Internal Revenue Service (IRS) audit. The best defense against these results is a good offense, namely avoiding errors on your return. Suppose that on the average 1998 individuals in 2,000 are free from the numerical errors in preparing their income tax return. If 10,000 forms are selected at random and examined, find the probability that 6, 7, or 8 of the forms will be in error. QUESTION A3 [5 marks} Netix is a good example of a big brand that uses big data analytics for targeted advertising. With over 100 million subscribers, the company collects huge data, which is the key to achieving the industry status Netix boosts. If you are a subscriber, you are familiar to how they send you recommendations of the next movie you should watch. With enough data, they can provide exactly 75% correct recommendation. Given in five reconnnendations, where X represents the number of non-recommended channel. (a) Construct the probability distribution modelling of X. (1 mark) (h) Calculate the probability that at least three of the ve recommendations is non- recommended channels. (4 marks)