Question:
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?