A continuous variable x is said to have a uniform distribution if the density function is given in attached image The corresponding density “curve” has constant height over the interval from a to b. Suppose the time (min) taken by a clerk to process a certain application form has a uniform distribution with a = 4 and b = 6. a. Draw the density curve, and verify that the total area under the curve is indeed 1. b. In the long run, what proportion of forms will take between 4.5 min and 5.5 min to process? At least 4.5 min to process? c. What value separates the slowest 50% of all processing times from the fastest 50% (the median of the distribution)? d. What value separates the best 10% of all processing times from the remaining 90%?
A continuous variable x is said to have a uniform distribution if the density function is given in attached image The corresponding density “curve” has constant height over the interval from a to b. Suppose the time (min) taken by a clerk to process a certain application form has a uniform distribution with a = 4 and b = 6. a. Draw the density curve, and verify that the total area under the curve is indeed 1. b. In the long run, what proportion of forms will take between 4.5 min and 5.5 min to process? At least 4.5 min to process? c. What value separates the slowest 50% of all processing times from the fastest 50% (the median of the distribution)? d. What value separates the best 10% of all processing times from the remaining 90%?
A continuous variable x is said to have a uniform distribution if the density function is given in attached image The corresponding density “curve” has constant height over the interval from a to b. Suppose the time (min) taken by a clerk to process a certain application form has a uniform distribution with a = 4 and b = 6. a. Draw the density curve, and verify that the total area under the curve is indeed 1. b. In the long run, what proportion of forms will take between 4.5 min and 5.5 min to process? At least 4.5 min to process? c. What value separates the slowest 50% of all processing times from the fastest 50% (the median of the distribution)? d. What value separates the best 10% of all processing times from the remaining 90%?
A continuous variable x is said to have a uniform distribution if the density function is given in attached image
The corresponding density “curve” has constant height over the interval from a to b. Suppose the time (min) taken by a clerk to process a certain application form has a uniform distribution with a = 4 and b = 6. a. Draw the density curve, and verify that the total area under the curve is indeed 1. b. In the long run, what proportion of forms will take between 4.5 min and 5.5 min to process? At least 4.5 min to process? c. What value separates the slowest 50% of all processing times from the fastest 50% (the median of the distribution)? d. What value separates the best 10% of all processing times from the remaining 90%?
Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.
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