2)- Industrial engineers periodically conduct "work measurement' analysis to determine the time required to produce a single unit of output. At a large processing plant, the number of total worker-hours required per day to perform a certain task was recorded for 50 days. The data are shown here: 128 119 95 97 124 128 142 98 108 120 113 109 124 132 97 138 133 136 120 112 146 128 103 135 114 109 100 111 131 113 124 131 133 131 88 118 116 98 112 138 100 112 111 150 117 122 97 116 92 122 a) Compute the mean, median, and mode of the data set. b) Find the range, variance, and standard deviation of the data set. c) Construct the interval yto, y± 2o, and y ± 30. Count the number of observations that fall within each interval and find the corresponding proportions. Compare the results to the Empirical Rule. Do you detect any outliers?
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!
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