A contractor is uncertain of the precise total costs for either materials or labor for a project. In addition, the total line of credit for financing the project is $260,000, and the contractor wants to know the probability that total costs exceed $260,000. It is believed that material costs can be represented by a normally distributed random variable with mean $100,000 and standard deviation $10,000. Labor costs are $1,500 a day, and the number of days needed to complete the project can be represented by a normally distributed random variable with mean 80 and standard deviation 12. Assuming that material and labor costs are independent, what are the mean and standard deviation of the total project cost (materials plus labor)? In addition, what is the probability that the total project cost is greater than $260,000?
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!
A contractor is uncertain of the precise total costs for either materials or labor for a project. In addition, the total line of credit for financing the project is $260,000, and the contractor wants to know the
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