2. (a) The data below is the annual sales, in millions of Ghana Cedis, for 21...
2. (a) The data below is the annual sales, in millions of Ghana Cedis, for 21 pharmaceutical companies in Ghana. 8408 1374 1872 8879 2459 11413 608 14138 6452 1850 2818 1356 10498 7478 4019 4341 739 2127 3653 5794 8305 i. Provide a five-number summary (5 marks] ii. Compute the lower and upper limits. [2 marks] iii. Do the data contain any outliers? [2 marks] iv. Show a box plot of the sales data. (5 marks] (b) In the daily production of a certain kind of rope, the number of defects per foot Y is assumed to have a Poisson distribution with mean 1 = 2. The profit per foot when the rope is sold is given by X, where X = 50 - 2Y - Y?. Find the expected profit per foot. (5 marks) (c) In an assembly-line production of industrial robots, gearbox assemblies can be installed in one minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be re-drilled. Twenty gearboxes are in stock, 2 with improperly drilled holes. Five gearboxes must be selected from the 20 that are available for installation in the next five robots. i. Find the probability that all 5 gearboxes will fit properly. [3 marks] ii. Find the mean and variance of the time it takes to install these 5 gearboxes. [3 marks)