QUESTION TWO (25 Marks) 2.1. Eighty percent of diamonds received from mine A are of superior quality, while only 50% of the diamonds received from mine Z are of superior quality. However, the manufacturing capacity of mine A is limited, and for this reason only 40% of the diamonds purchased come from mine A. An incoming shipment of diamonds is inspected, and found to be of superior quality. What is the probability that it comes from mine A? (6 marks) 2.2. If 40% of all patients have medical aid, what is the probability that in a sample of 10 patients: 2.2.1. exactly six have medical aid? (3 marks) 2.2.2. at most two have medical aid? (5 marks) 2.3. The Faber Co. produces a pencil called Ultra-Lite. It is expected that sales will follow a normal distribution, with a mean of 457 000 pencils each year. 90% of the time, sales have been between 454 000 and 460 000 pencils. Estimate the standard deviation of this distribution. (6 marks) 2.4. The machine repair department of Scorpio Press receives an average of 2 calls for service per hour. What is the probability of receiving no service calls in a 45 minute period