Quantitative Analysis for Business

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MANAGEMENT COLLEGE OF SOUTHERN AFRICA (MANCOSA) ASSIGNMENT COVER SHEET SURNAME FIRST NAME/S STUDENT NUMBER MODULE NAME

: MONDO : ANNITA : 117749 : QUANTITATIVE METHODS

ASSIGNMENT NUMBER : 1 (ONE) TUTOR S NAME : MR MUPAMBIREYI

EXAMINATION VENUE : UNIVERSITY OF ZIMBABWE DATE SUBMITTED SUBMISSION POSTAL ADDRESS E-MAIL CONTACT NUMBERS : 26 SEPTEMBER 2011 : 1 ST SUBMISSION : 156 WAJETSI WAY, LETOMBO PARK, HARARE : mondoa@dairibord.co.zw : WORK MOBILE COURSE / INTAKE DECLARATION I hereby declare that the assignment submitted is an original piece of work produced by myself. SIGNATURE : AMONDO DATE: 26/09/11 : +263 4 779050-9 : +263 772 385 493 JANUARY 2011

: MBA YEAR 1

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Contents Question 1......................................................................................................................................... 3 Question 2......................................................................................................................................... 8 Question 3....................................................................................................................................... 14 Question 4....................................................................................................................................... 17 Question 5....................................................................................................................................... 21

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Question 1

Range = maximum minimum =158 =137 Therefore class interval = maximum minimum Number of classes = 137 5 = 27.4 = 30 21

The interval rounded off

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Stem and Leaf 2 3 4 5 6 7 8 9 10 11 12 14 15 1 0 0 0 1 0 2 0 0 1 3 5 0 5 7 4 1 1 4 3 2 6 9 6 8 9 6 4 3 4 4 7 8 3 6 4 9 6 5 9

Table 1.1 Frequency Distribution Table Class MidClass Tally point Less Frequencies cumulative (f) frequency than

20 50 50 80 80 110 110 140 140 170

IIII I IIII IIII II IIII IIII IIII IIII IIII

35 65 95 125 155

6 12 14 4 4

6 18 32 36 40

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1.2.1 Histogram

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1.2.2 Frequency Polygon

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1.2.3 Less- than Ogive (Graph also showing solutions for 1.3.1 and 1.3.2)

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Question 2
Table 2.1 Daily Trading volumes (million shares) for stocks x 917 983 1046 944 723 783 813 1057 766 836 992 973 10833 x-x 14.25 8025 143.25 41.25 -179.75 -119.75 -89.75 154.25 -136.75 -66.75 89.25 70.25 (x-x ) 2 203.06 6440.06 20520.56 1701.56 32310.06 14340.06 8055.06 23793.06 18700.56 4455.56 7965.56 4935.06 143420.22

2.1 Mean = X n

=

10 833 12

=

902.75 million shares

S2

=

(x- x) 2 n-1

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=

143420.22 12-1

=

143 420.22 11

=13 038.20

= =

13 038.20 114.18 million shares

2.2 Z = x-µ

Where x µ

= = = =

a specific value in the data set (800) population mean (902.75) population standard deviation (114.18) 800 902.75

114.18 = 0.90

The sketch below illustrates the area under investigation. Figure 2.2.1 solving for B

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A +B = B =

0.5 0.5 A

Value of A from the z distribution table is 0.3159 Therefore B = = 0.5 -0.3159 0.1841

2.3 As shown above, Z = x-µ

=

1 000 902.75 114.18

Z

=

0.85

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Shown in the sketch, Figure 2.3.1 Solving for B

A +B = B =

0.5 0.5 A

Value of A from the z-distribution table is 0.3023 Therefore B = 0.1977

2.4

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Z

=

x-µ

=

0.05 114.18

902.75

= x = =

0.05 x 114.18 =

x 902.75

0.05 x 114.18 + 902.75 5.709 + 902.75

Figure 2.4.1 Solving for x

A+B = A = = = Therefore x
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0.5 0.5 - B 0.5 0.05 0.45 (from the z- distribution) 902.75 + 1.65 (114.18)

=

=

1091.08

Therefore 1091 billion shares will trigger a press release

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Question 3
Table 3.1 number of rented cars Hertz 2007 30 28.91 2008 29 30.13 2009 Total 32 31.96 91 Avis 25 24.78 23 25.83 30 27.39 78 National Budget Other 20 16.84 18 17.55 15 18.61 53 14 17.47 20 18.21 21...
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