Standard deviations/mean/ normal distribution?

Question

The financial manager is investigating the collection of debts under £1000 from various individuals and companies. Her investigation, so far, has revealed that the amount of the debts still awaiting payment (750 debts in total) follows a normal distribution with a mean debt of £400 and a standard deviation of £100
She is currently considering the following plan of action:
a) write off all debts under £200
b) send a letter by ordinary post, demanding payments for all debts between £200 and £350.
c) send bailiffs to collect the payment for all debts over £600

She has also calculated the following costs:
i) writing and sending a letter by ordinary post costs £25,
ii) sending the bailiffs costs £225

The success, in terms of money collected as a result of action taken, varies in the following way:

d) 85% of debts between £200 and £350 are paid
e) 100% of debts over £600 are paid

Include in your final report an analysis of her plan of action. Providing a clear breakdown of costs and payments collected. Investigate the effects of changes in costs and give advice on where best to make changes and place emphasis so that the company has a better record in this area.

Please anyone give me pointers on how to go about this problem, much appreciated.

Anonymous · Accepted Answer

Will you accept American advice?  Given our current economic mess, we may have to give ourselves back to the Queen!   heh  heh  heh

Consider marginal costs for each of the four groups:

1 of 4:   600-  ??? debt
2 of 4:   350 - 599 debt
3 of 4:   200 - 350 debt
4 of 4:      1 - 199 debt

We know the correct course of action for groups
1 and 3.  How?  Because the marginal profit
exceeds the marginal cost in both cases.

600 - 225 bailiff fee = 375 profit (100% of the time)
350 - 25 postal fee = 325 profit (85% of the time)
200 - 25 postal fee = 175 profit (85% of the time)

So that much is settled.  But here is the rub:

What about groups 2 and 4?  In group 2, we could 
reasonably assume a profit.  However this is not certain.
That's because we assume a bailiff would scare
the 351-599 crowd as much as the bailiff scares the
600+ crowd.  If the bailiff does so, then group 2
is also profitable when you send the bailiff.
(351-225 = 126 profit and 599-225 = 374 profit).

But what about the "lower classes"?    Of course,
we don't have classes in America.  heh  heh  heh

But if we did, the key would be the success rate
of sending the postal letter.  It would be unprofitable
to send a 25 letter to someone who owes only 24.
On the other hand, sending a 25 letter to someone
who owes 199 would almost certainly be profitable.


Sorry.  Boss coming.  Cannot finish answer.
Must get back to work now before I get sacked
and go into debt!


Good luck!
Ron

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Standard deviations/mean/ normal distribution?

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