Question 1: 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
|
a) Using seven classes of equal width organize the above data as a less-than cumulative frequency distribution.
b) Draw to scale the less-than ogive for the above data.
c) Use the ogive to determine:
d) The percentage of apartments for which the electricity cost is in the range $115 - $135.
e) The mid- 75 percentage range.
Question 2:
a) 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.
i) If a new bond is to be issued by a city, what is the probability that it will receives an A rating?
ii) What proportion of municipal bonds is issued by suburbs?
b) 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.
i) What is the probability that a randomly selected visit will last between 60 and 90 minutes?
ii) Less than how many minutes will only 20% of the visits last?
iii) Between what values, symmetrically distributed around the mean will 90% of visits last?
Question 3:
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:
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
|
a) Draw to scale a time series graph representing the above data.
b) Using the ratio-to-moving-average method, determine the quarterly seasonal indices.
c) Interpret the quarterly pattern of enrolment
d) Compute the trend equation.
e) Forecast the 2011 enrolment by quarter.
Question 5:
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.