The length of time Y necessary to complete a key operation in the construction of houses has an exponential distribution with mean 15 hours. The formula C= 100 + 50Y+ 3Y relates the cost Cof completing this operation to the square of the time to completion. The mean of Cwas found to be found to be 2,200 hours and the variance of C was found to be 13,725,000. How many standard deviations above the mean is 3,000 hours? (Round your answer to two decimal places.) Would you expect C to exceed 3,000 very often? Three thousand is a large number of standard deviations from themean and therefore indicates that values exceeding 3,000 would not be uncommon. O Three thousand is a small number of standard deviations from the mean and therefore indicates that values exceeding 3,000 would not be uncommon. O Three thousand is a large number of standard deviations from the mean and therefore indicates that values exceeding 3,000 would be uncommon. O Three thousand is a small number of standard deviations from the mean and therefore indicates that values exceeding 3,000 would be uncommon.

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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!