Heading 3 Normal TQitem TQpart TQparttext Paragraph Styles Section B Question B.1 [6 marks] There are seventy-five applicants for an MBA program. One of the criteria to rank applicants is the score of the GMAT test. The GMAT test assesses different skills of the applicants such as analytical and verbal skills. The GMAT test is scored from 200 to 800. More specifically, historical data show that the mean GMAT score is 444 98 while the standard deviation is 102.07. Based on the above information, what is the probability that a student will: (a) Score more than 706? [3 marks] (b) Score less than or equal to 526? [1 mark] (c) Score between 526 and 706? [2 marks] Round your answers to four decimal places. Question B.2 [24 marks] A quality control engineer of a manufacturing company within the automotive industry has the task of monitoring whether the diameter of the engine valves for a specific car type conform to specifications. Specifically, the diameters of these valves are normally distributed On average the diameter is equal to 27.87. In half an hour 10 valves are produced (a) If the standard deviation of the entire process is known to be equal to 0.035, D Focus ES - 12 - A Aa-POE EEEEN 4 21 T | -b *, * A-DATEIE AaBbcc AaBbCc ) AaBt (a) AaB AaBbcc Heading 3 11 Normal 1 Qitem TQpart 1 Qparttext Font Paragraph Styles Question B.2 [24 marks] A quality control engineer of a manufacturing company within the automotive industry has the task of monitoring whether the diameter of the engine valves for a specific car type conform to specifications. Specifically, the diameters of these valves are normally distributed. On average, the diameter is equal to 27.87. In half an hour, 10 valves are produced (a) If the standard deviation of the entire process is known to be equal to 0.035, please compute: 0 The lower limit of a 90% confidence interval [2 marks] (m) The upper limit of a 90% confidence interval. [2 marks] (iii) The lower limit of a 95% confidence interval. [2 marks] (iv) The upper limit of a 95% confidence interval. [2 marks] (v) The lower limit of a 99% confidence interval. [2 marks] (vi) The upper limit of a 99% confidence interval [2 marks] D English (Ireland Focus BO 12 AA AA EEEEEAUT * * A-DA AaBbcc AaBbCd (0) AaBt (a) AaB AaBbcc Heading 3 1 Normal 1 Qitem TQpart Qparttext Font Paragraph Styles (b) If the standard deviation of the sample is known to be equal to 0.075, please compute: 0 The lower limit of a 90% confidence interval. [2 marks] () The upper limit of a 90% confidence interval. [2 marks] (ii) The lower limit of a 95% confidence interval [2 marks] (iv) The upper limit of a 95% confidence interval. [2 marks] (v) The lower limit of a 99% confidence interval [2 marks] (vi) The upper limit of a 99% confidence interval [2 marks] Round your answers to four decimal places. Question B.3 [20 marks] A manufacturing company in the electronic devices field is highly satisfied with the volume of sales of its smart TVs. Historical data suggest that the average profit is