Example 4.10 Distillation towers are used by chemical industries including petroleum refineries for distillation purposes. With all the advances in distillation technology, failure rate in distillation towers is expected to be on the decline. To identify the trend, Kister (IChemE, 2003) collected data on 900 cases and studied causes of malfunc- tions among such towers. The data identified plugging/coking as the undisputed leader of tower malfunction. Figure 4.10 describes the breakdown of causes of plugging stratified by the year of malfunction recorded as prior to 1992 (1992) and 1992 or later (1992+). Suppose a tower were selected at random from the records prior to 1992. What is the probability that the selected tower had plugging because of (a) coking, (b) precip- itation, (c) polymer, (d) coking and polymer. What are these probabilities for a tower selected at random from records 1992 or later? Example 1.14 A lawnmower manufacturer provides several different lines of lawnmowers to businesses. The mean and standard deviation of prices of their lawnmowers are $500.00 and $125.00, respectively. In response to increase in petroleum prices that led to increased transportation costs, the manufacturer decided to increase the prices of its products. Two different schemes were proposed as follows: A Increase the price of each lawnmower by $50.00. B Increase the price of each lawnmower by 10%. a For each of these two schemes, determine the mean and standard deviation of the new prices. b Explain the effect of each scheme on the prices of the lawnmowers