Question 3 Currently you are enrolled for the module Operational Research III in your studies towards the National Diploma in Industrial Engineering. The lecturer awards a mark from an A to F. Thus, you can obtain a mark expressed as A, B, C, D or F. The distribution of marks awarded for the past 2 years is represented in the table below: Marks awarded Number of students A 80 B 75 90 D 30 F 25 Total 300 If this past distribution is a good indicator of future marks, you are required to compute the probability of you receiving a C grade in the module. [9] Question 4 You have recently qualified as an Industrial Engineer and found employment at an organisation manufacturing nails. The company manufacture quality nails in lengths of 1 inch, 2-inch, 3-inch, 4-inch and 5-inche for various uses. Management requested you to investigate quality issues. During your investigation you have found an overrun occurs where nails are slightly defective. The defective nails are placed in a common bin and is sold to the public. In yesterday's production run, 651 of the 1-inch nails, 243 of the 2-inch nails, 41 of the 3-inch nails 451 of the 4- inch nails and 333 of the 5-inch nails was placed in the bin. To advance tour investigation, you would like to determine the probability of finding a certain length of nail if you reach into the bin. Compute the probability that: a. Reaching into the bin you will find a 4-inch nail. (8) b. Reaching into the bin you will find a 5-inch nail. (2 14 OPR371S/101/0/2021 c. If a certain application requires a nail that is 3 inches or shorter, that you will be able to satisfy the requirement of the application. What is the conclusion that can be drawn from the information? (5) [15]