MANCOSA: MBA (GENERAL) YEAR 1
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ASSIGNMENT 5: QUANTITATIVE METHODS
QUESTION 1 (21) A large shipping company recorded the tonnage shipped weekly across the pacific for 50 weeks. The data is presented in the table below. L1-14- S79 4'39 44310 Lt. 2.,"7 So c 4 (7
530 492 462 379 487 523 600 618 548 431 596 521 414 607 662 618 423 573 509 690 666 403 544 545 526 620 507 630 537 385 440 383 489 402 439 554 532 427 548 417 574 634 466 422 562 436 504 597 641 639
h,c, ccw,, t14,4- 100
L 62-6 (3c) 636 t,n
c7010 — 2-79
1.1 Using seven classes of equal width, arrange the above data in a less-than cumulative distribution. Let 350 tonnes be the lower limit of the initial class. (8) 1.2 Use the distribution in 1.1 to calculate the lower quartile and the mode. (4) 1.3 Draw, to scale, the less-than ogive for the distribution obtained in 1.1. (4) 1.4 Use the graph drawn in 1.3 to determine the mid-70% range. (5)
QUESTION 2
(18) The production department of a leading newspaper has embarked on a quality improvement effort and has chosen as its first project an issue that relates to the blackness of the newspaper print. Each day a determination needs to be made concerning how "black" the newspaper print is. The blackness of print is measured on a standard scale in which the target value is 1.0. Data collected aver the past year indicate that the print blackness is normally distributed with an average of 1.01 and a standard deviation of 0.12. Each day, one printed spot on the first newspaper printed is chosen randomly and the blackness of the spot is measured. Suppose the blackness of print is considered acceptable if the blackness of the spot is between 0.95 and 1.05.
2.1 Calculate the probability that the blackness of the spot is: 2.1.1 between 0.95 and 1.0? (5) 2.1.2 less than 0.95 or greater than 1.05? (2)
2.2 If the objective of the production team is to reduce the probability that blackness is below 0.95 or above 1.05, would it be better to focus on process improvement that lowered the blackness to the target value of 1.0 or on process improvement that reduced the standard deviation to 0.08? Justify your answer quantitatively. (6)
2.3 Each day, a random sample of 25 printed spots is chosen and the blackness of the spots is measured. Assuming that the distribution of blackness has not changed from what is was previously, what is the probability that the average blackness of the spots is less than 0.95 or greater than 1.05? (5)
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PROGRAMME HANDBOOK: JANUARY 2016 INTAKE