Question

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)

Answer 1

Dear student, we can provide you with the solution of 4 sub question at a time.

a)

B 5 Book1 - Excel Gurvinder Singh X File Home Insert Page Layout Formulas Data Review View Help Tell me what you want to do Ie> Calibri Vl11 VÅ A ab Wrap Text General & Cut Eg Copy Format Painter AM HH LO & Share AutoSum- AY O Fill - Sort & Find & Clear - Filter - Select- Editing Paste BI U - -A === Merge & Center % , 4.0 .00 5.0 Insert Delete Format Conditional Format as Cell Formatting Table Styles Styles Number Cells Clipboard Font Alignment EXPERIENCE MICROSOFT 365 Keep your files safe, secure, and accessible with 1 TB of cloud storage. Try Microsoft 365. Start free trial X Q15 > for A B с D E G F -- H J K L M N o P o R 1 2 608 739 1356 ii) Lower limit= Upper limit = Q1-1.5(IQR) -7777.5 Q3+1.5(QR) 17954.5 D17-1.5*D19 D18+1.5*D19 3 4 1374 1850 5 6 1872 iii) There is no outlier present, as the data is sorted and no value is outside the limit calculated above Chart Title iv) Box Plot 16000 7 2127 2459 8 9 2818 14000 10 3653 12000 Columni a) i) Mean 5170.524 Standard Error 854.9194 Median 4019 Mode #N/A Standard Deviation 3917.733 Sample Variance 15348630 Kurtosis -0.3911 Skewness 0.7485 Range 13530 Minimum 608 Maximum 14138 Sum 108581 Count 21 First quartile 1872 Third quartile 8305 IQR 6433 11 10000 12 4019 4341 5794 6452 13 8000 6000 7478 14 15 16 17 4000 2000 8305 8408 8879 10498 11413 QUARTILE.INC(A1:A21,1) QUARTILE.INC(A1:A21,3) 18 0 1 19 20 21 14138 Sheet1 Sheet2 Sheet3 + Ready B + 100% Type here to search о j c 1) ENG 06:46 31-07-2020