Judith Lewis is a doctoral student at State University, and she also works full-time as anacademic tutor for 10 scholarshiped student athletes. She took the job, hoping it would leaveher free time between tutoring to devote to her own studies. An athlete visits her for tutoring an averageof every 16 hours, and she spends an average of 1.5 hours (exponentially distributed) withhim or her. She is able to tutor only one athlete at a time, and athletes study while they are waiting. a. Determine how long a player must wait to see her and the percentage of time Judith is busy. Does the job seem to meet Judith’s expectations, and does the system seem adequate to meet the athletes’ needs? b. If the results in (a) indicate that the tutoring arrangement is ineffective, suggest an adjustment that could improve it for both the athletes and Judith.
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!
Judith Lewis is a doctoral student at State University, and she also works full-time as an
academic tutor for 10 scholarshiped student athletes. She took the job, hoping it would leave
her free time between tutoring to devote to her own studies. An athlete visits her for tutoring an average
of every 16 hours, and she spends an average of 1.5 hours (exponentially distributed) with
him or her. She is able to tutor only one athlete at a time, and athletes study while they are waiting. a. Determine how long a player must wait to see her and the percentage of time Judith is busy.
Does the job seem to meet Judith’s expectations, and does the system seem adequate to meet
the athletes’ needs?
b. If the results in (a) indicate that the tutoring arrangement is ineffective, suggest an adjustment
that could improve it for both the athletes and Judith.
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