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.

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.

Question 4:

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

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.