A restaurant buys avocados from three suppliers P, Q and R. Records showthat 30% of the avocados come from P, 55% come from Q and the rest come from R. Further records show that 8% of avocados supplied by P are substandard, 12% of avocados supplied by Q are substandard and 15% of avocados supplied by R are substandard. (5 Marks) A chef working at the restaurant randomly selects an avocado and finds it to be substandard. Calculate the probability that this avocado came from supplier Q. The manager of the restaurant notices that customers arrive at the restaurant at an average rate of 10 customers per hour. Assume a Poisson distribution. 2.1 Determine the probability that exactly 7 customers arrive in a given hour. 2.2 Determine the probability that at least 2 customers arrive in a given 15-minute period. Customers at the restaurant have to wait an average of 25 minutes before they receive their meal from the time their order was placed. Assume these waiting times are normally distributed with a standard deviation of 5 minutes. 3.1 What is the probability that a randomly selected customer waits between 20 and 35 minutes before receiving his meal from the time his order was placed? 3.2 What is the maximum waiting time for a customer to receive her meal if she is in the 10% of customers who receive their meals in the fastest time from when the order was placed? (4 marks) (8 marks) (6 marks) (7 marks)