Business Mathematics_case_1

Business Mathematics Case Study

Study Questions and answers

Question 1 : What was Lee sketching on notepad ?

Solution : Here the word sketching does not means here – most probably (again probability ) - drawing funny faces ; but being a manager Lee was drafting the future strategy depending upon data available i.e. calculating his priory probabilities.

Question 2 : What type of calculation will Lee make and what additional
information will be needed?

Solution: Being a good data collector and interpretator (as mentioned in
first paragraph of case study ) Lee seems to have a good knowledge of mathematics . And in mathematics one of the best tool available to predict the futuristic occurrences based upon some , may be incomplete, information is the use of Probability theory . More concisely the Addition theory of probability and Baye’s Theory of probability, as the case may be. The best application of Baye’s theorem is in revising priory probabilities. Practically, many times while predicting for something, with passage of time and some initial results in hands, we need to alter our priory probabilities. So the new probabilities are called revised probability or posterior probability. Here there is probability of work being stopped given any of the following occurs :
1) Cold and Flu bug hits .
2) Bad snow storm strikes.
Hence need for calculation of conditional probability i.e.
to use the Baye’s theorem.
But in this case, the data provided is not sufficient. What is provided is that there is probability of delay in completion of job due to snow storm and hence to cover the losses there is no provision of scheduling weekend work as it would cost a time – and- half on wages. So what is not provided is how much is that actual time.


Question 3: What differences will it make if Nancy’s definition of
“Reasonably Certain” means to meet the required production
goal “75 percent of time” or “99 percent of time” ?

Solution :
Part 1 : The probability of no of days of work being stopped given any of the following occurs :
1) Cold and Flu bug hits is 1/30 [ P(a) ]
2) Bad snow storm strikes is 2/30 [ P(b) ] (case study says this to be “may be”
But for the sake of some conclusion we are assuming it to be certain)

Both the events are mutually exclusive – occurrence of one does not depend upon happening of other.
So applying Addition theory of Probability
P(a U b) = P(a) +P(b)
So probability of work being stopped due simultaneous occurrence of both the events is = 1/30 + 2/30

ð P(a U b) = 3/30
ð = 1/10
ð Hence chaces are that 10 % of working days being lost s
ð Out of 19 days available 1.9 days ≈ 2 days gone.
ð Most possibly, Total days available 17
ð If Martin Luther King Day holiday is provided then total days available is 16.


Part 2 : Total days required to complete the job =17
ð Job done in 1 day is 1/17 o the job
ð Job done in 16 days = 16/17
ð 16/17=94 % of the job
ð So we can conclude that taking account of all the given conditions ,there is probability of completion of 94 % job.

So if Nancy defines “reasonably certain” as achieving 75% of the production goal
She can relax but if it to be 99% better she should not give Martin Luther King Day holiday.

☺