Copying Statistics Probability Distributions and Research Proposal

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This, in turn, can tell us how likely it will be to experience higher than average volumes of service calls on any given day.

The standard deviation for office-use copier repairs is nearly nine, while for professional-use copiers it is about four. According to the normal distribution, there is an 84% chance that an outcome will be lower than one standard deviation higher than the average. For example, adding the standard deviation nine to the average of forty-three repairs gives us fifty-two repairs; on only 16% of working days would we expect to see a higher rate of service calls. Therefore, seven technicians can handle the work 84% of the time -- an adequate number. Applying this same method to the professional copier situation reveals that twenty-four service calls or less will come in 84% of the time, and six technicians can cover this. So a total of thirteen technicians seven for office use and six for professional-use copiers, ought to be plenty to ensure speedy service to customer without employing too many idle technicians.

After the acquisition, the change in numbers obviously calls for a reassessment. Te claim that a 50% increase in copiers requires a 50% increase in technicians can easily be tested by applying the same mathematic principles and functions.

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3185 office-use copiers will result in an average of 65.4 service calls and a standard deviation of 13.4, meaning 69 service calls or less will come in 84% of the time, requiring nine technicians. 596 professional use-copiers have an average of 30.6 calls a day and a standard deviation of 6.2, for a total of 39 calls or less 84% of the time, requiring ten technicians. These numbers indicate that two more office-use and four more profession-use technicians should be hired after the acquisition than should ideally be employed now, which shows that the law of averages is correct in predicting that the number of service call "explosions" evens out as the number of copiers increases. Though there is an approximately fifty-percent increase in the number of copiers acquired, less of an increase is necessary in the number of technicians hired.

To err on the side of even faster service, more technicians could of course be hired. Adding another standard deviation's worth of repair calls and hiring the attendant number of technicians would mean that the company was covered almost 98% of the time. It would also mean hiring four more technicians -- two more each for office-use and professional-use copiers, and there would be a great deal more idle time......

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