According to records kept by Mariposa County, the average (mean) amount of time that it takes for employees to be reimbursed for professional expenses incurred in service to the county is 36 days, with a standard deviation of 5 days. The distribution is normal. The head of the Mariposa County Accounting Department wants to establish a standard regarding the length of time that employees can expect to wait to receive reimbursement for professional expenses. She wants to publish a standard that states the number of days it takes the department to process 98% of the claims filed. Help the department head find that standard.
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!
According to records kept by Mariposa County, the average (
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