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Question 3 Penicillin is produced by the Penicillium fungus, which is grown in a broth whose sugar content must be carefully controlled. The optimum sugar concentration is 4.9 mg/mL. If the concentration exceeds 6.0 mg/mL, the fungus dies and the process must be shut down for the day. i) If sugar concentration in batches of broth X is normally distributed with mean 4.9 mgfrnL and standard deviation 0.6 mg/mL, what is the probability that the process will shut down? (3 marks) ii) The supplier offers to sell broth Y with a sugar content that is normally distributed with mean 5.2 mg/mL and standard deviation 0.4 mg/mL. Will broth Y result in fewer days of production lost than broth X? Explain (4 marks) QUESTION 4 A procurement specialist has purchased 35 resistors from vendor l and vendor 2. Each resistor's resistance is measured as shown in the table. Assume that the population standard deviation from vendor 1 and vendor 2 are unknown. By taking the significance level, a = 0.05, answer the following questions. Vendor 1 99.8 100.0 90.3 96.5 95.3 95.2 105.7 98.9 102.1 105.7 97.7 99.7 103.1 96.6 103.9 105.0 95.4 109.8 109.1 98.6 99.8 97.6 97.3 98.2 96.7 99.8 105.3 103.7 103.5 1 10.4 99.5 105.4 98.5 96.5 99.4 Vendor 2 107.8 1 14.7 109.0 106.2 109.2 106.7 106.7 103.0 105.2 105.6 109.3 100.4 109.0 106.5 109.9 103.5 106.2 102.8 106.2 110.5 108.8 101.3 112.2 102.7 109.5 108.4 113.5 104.3 109.8 111.5 106.8 105.4 116.3 108.7 112.3 (3) Calculate the mean and standard deviation for both vendors. (4 marks) (b) Perform an appropriate statistical hypothesis testing to determine whether the procurement specialist can claim that the mean of resistance from vendor 1 is significantly different from the mean resistance of vendor 2. (6 marks) (c) If you were the procurement specialist and you were about to select only one vendor in the future, which vendor will you choose to purchase the resistors? Give your justications with appropriate statistical test. (6 marks) (d) Construct a 95% condence interval on the difference in mean resistance for the two vendors. (4 marks)