Exercise 1: Canada's sugar industry is an integral part of Canadian history, and a value- added success story. Currently, there are three cane sugar refineries in Canada. Suppose that a Canadian sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of raw sugar (in tons) that one plant can process in one day can be modeled using an exponential distribution with mean of 4 tons for each of three plants. Assume that each plant operates independently. 1. On a given day a plant has processed more than a ton of raw sugar. What is the probability that a plant will process 4 more? 2. Find the probability that exactly two of the three plants process more than 4 tons of raw sugar on a given day. 3. How much raw sugar should be stocked for the plant each day so that the chance of running out of the raw sugar is only 0.05?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 10 images
