Question

A shoe repair shop has one large motor supplying power to 8 workers. Each worker needs the power 24 minutes every hour on average, so that his chance of needing power at any given moment is 24/60 = 40%. And each worker works independently of the other workers. That is, at any given moment his chance of drawing power does not depend on whether his co-workers happen to be drawing power.

a. At any moment, what is the chance that all 8 workers would happen to need power? And what is the average number who need power?

b. If the motor’s capacity is limited to 3 workers drawing power at once, what is the proportion of time it will be overloaded?

c. Management wants this overload to occur only 5% of the time, at most. To what level must they increase the capacity of the motor (i.e., how many workers should the motor allow to draw power at once)?

Answer 1

(a) The case can be written as a binomial distribution ( a+b)ⁿ where

a = probability of power demand =0.4

b = Probability that the power is not demanded =1-0.4 =0.6

n = No. of units demanding power

The probability that m units will demand the power is