The average (mean) amount of time that a manager at the Cimaron Valley 7.2 Department of Human Services spends in the annual performance review with an employee is 31.3 minutes, with a standard deviation of 5.7 minutes (normal distribution). What percentage of the annual performance reviews in the depart- ment take between 24.9 and 36.1 minutes? Between 26.4 and 30.6 minutes? Between 32.0 and 37.5 minutes? What percentage of the annual performance reviews take more than 40 minutes? What percentage take less than 20 minutes?
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!
Can you please help answer the rest of the questions in problem one? Starting with What percentage of the annual performce reviews take morevthan 40 mintues? What percentge take less than 20 minutes? These questions are part of a thing call Z scores, the
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