The data displayed below represents the electricity cost during a recent month for a random sample of 50 one-bedroom apartments in a large city. 96 171 202 178 147 102 153 197 127 82 157 185 90 116...

The data displayed below represents the electricity cost during a recent month for a random sample of 50 one-bedroom apartments in a large city.

96	171	202	178	147	102	153	197	127	82
157	185	90	116	172	111	148	213	130	165
141	149	206	175	123	128	144	168	109	167
95	163	150	154	130	143	187	166	139	149
108	119	183	151	114	135	191	137	129	158

1.1 Using seven classes of equal width organize the above data as a less-than cumulative frequency distribution. (7)
1.2 Draw to scale the less-than ogive for the above data. (4)
1.3 Use the ogive to determine:
1.3.1 The percentage of apartments for which the electricity cost is in the range $115 - $135. (3)
1.3.2 The mid- 75 percentage range. (5)

Question 2 (22)


2.1 A municipal bond service in the US has three rating categories (A,
B
and
C). Suppose that of the total number of municipal bonds issued in the past year, 70% were rated
A, 20% were rated
B
and 10% were rated
C. Of the bonds rated
A, 50% were issued by cities, 40% by suburbs and 10% by rural areas. Of the bonds rated
B, 60% were issued by cities, 20% by suburbs and 20% by rural areas. Of the bonds rated
C, 90% were issued by cities, 5% by suburbs and 5% by rural areas.
2.1.1 If a new bond is to be issued by a city, what is the probability that it will receives an
A
rating? (5)
2.1.2 What proportion of municipal bonds is issued by suburbs? (3)
2.2 Unisys.com is one of the most frequented business-to-business web sites. According to a Wall Street Journal article, business partners accessing Unisys.com spend an average of 65.7 minutes, possibly the longest average time per visit of any business-to-business Web site. Assuming that the duration of a visit to this Website is normally distributed with a mean of 65.7 minutes and a standard deviation of 15 minutes.
2.2.1 What is the probability that a randomly selected visit will last between 60 and 90 minutes? (4)
2.2.2 Less than how many minutes will only 20% of the visits last? (4) 2.2.3 Between what values, symmetrically distributed around the mean will 90% of visits last? (6)

Question 3 (14)


The table below gives two samples selected from 10 supermarkets of the weekly sales of a popular soft drink. The first sample gives the details for a normal shelf display of the product, while the second sample gives the details for an end-aisle shelf display. Assuming equal variances, establish, at the 5% level of significance, whether there is a statistically significant difference in the mean weekly sales for the two display locations.

Normal display	End-Aisle Display
22	52
34	71
52	76
62	54
30	67
40	83
64	66
84	90
56	77
59	84

Question 4 (25)


The table below gives the quarterly enrollment in a major American business college for the period 2007-2010.

Year	Winter	Spring	Summer	Autumn
2007	2033	1871	714	2318
2008	2174	2069	840	2413
2009	2370	2254	927	2704
2010	2625	2478	1136	30

4.1 Draw to scale a time series graph representing the above data. (4)
4.2 Using the ratio-to-moving-average method, determine the quarterly seasonal indices. (9)
4.3 Interpret the quarterly pattern of enrolment. (2)
4.4 Compute the trend equation. (6) 4.5 Forecast the 2011 enrolment by quarter. (4)

Question 5 (20)


A businessman has two independent investments
A
and
B
available to him, but he lacks the capital to undertake both of them simultaneously. He can choose to take
A
first and then stop, or if
A
is successful then take
B, or vice versa. The probability of success on
A
is 0.7 while for
B
it is 0.4. Both investments require an initial capital outlay of $2000 and both return nothing if the venture is unsuccessful. Successful completion of
A
will return $3000 (over cost), while successful completion of
B
will return $5000 (over cost). Prepare a report, with the aid of a decision tree, advising the investor of the best course of action.
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Instructions


1. Start each solution on a new page.
2. A spreadsheet (eg. Microsoft Excel) may be used only for the purposes of setting up tables, drawing of sketches and so forth. All solutions must be clearly shown through the use of appropriate formulae and substitution.
3. Solutions generated by software packages will not be marked.
4. No marks will be awarded if only the final answers are given. All relevant working must be shown.
5. The assignment must be typed using text font Arial or Times New Roman (size 11pt, 1½ lines spacing).
6. It is not necessary to provide references or a bibliography. Simply number each solution according to the numbering in assignment handbook.

NOTE:
This instruction applies ONLY to QUANTITATIVE METHODS and NOT to the other modules.