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Quantitative Techniques – I

Notes

Case Study Rattle Publishing Company Limited

attle Publishing Company Limited are planning to introduce a new ABC text-
book. The company’s marketing department estimates that the prior distribution
Rfor likely sales is normal with a mean of 10,000 books. In addition it has determined
that there is a probability of one half that the likely sales will lie between 8,000 and 12,000
books.
The text-book will sell for 10 per copy but the publishing company pays the author 10%
of revenue in royalties and the fixed costs of printing and marketing the book are calculated
to be 25,000. Using current printing facilities, the variable production costs are 4 per
book. However, the Rattle Publishing Company has the option of hiring a special machine
for 14,000 which will reduce the variable production costs to 2.50 per book.

Required:
1. Show that the standard deviation of likely sales is approximately = 3,000.
2. Using = 3,000 determine the probability that the company will at least break even
if:
(a) existing printing facilities are used,
(b) the special machine is hired
3. By comparing expected profits, decide whether or not the publishing company
should hire the special machine.
4. By using the normal distribution it can be shown that the following probability
distribution may be applied to book sales:
Sales (‘000) 0-5 5-8 8-10 10-12 12-15 15-20
Probability 0.05 0.20 0.25 0.25 0.20 0.05
By assuming that the actual sales can only take the midpoints of these classes, determine
the expected value of perfect information and interpret its value.

15.7 Summary

The normal probability distribution occupies a place of central importance in Modern
Statistical Theory. This distribution was first observed as the normal law of errors by the
statisticians of the eighteenth century.

Random variables observed in many phenomena related to economics, business and
other social as well as physical sciences are often found to be distributed normally.

Here and e are absolute constants with values 3.14159.... and 2.71828.... respectively.
This distribution is completely known if the values of mean and standard deviation
are known. Thus, the distribution has two parameters, viz. mean and standard deviation.
We seldom encounter variables that have a range from to , nevertheless the curves
generated by the relative frequency histograms of various variables closely resembles
the shape of normal curve.

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