Originally Posted by

**Kiwigirl** Silica Tech sell Hercules P150 desktop computer for $2400 (includes GST). The owner has kept a record of the number of computers, n, sold per week and the results are shown in this probability distribution (This is a table, but I don't know how to create a table on a thread, I think you will get the idea):

N............1......2......3.....4

P(N = n).. 0.1...0.2...0.3...0.4

The expected sales each week:

1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4 = 3.

The calculated variance of the sales each week = 1.

The fixed costs of the business (salaries, rent, power and so on) are $900 per week and the profit per computer is $375.

So, the expected profit each week:

375 (1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4) - 900 = 225.

a) Find the variance in profit each week.

$\displaystyle

\mathrm{Var}(prof)=\frac{1}{n}\sum_{i=1}^n (prof_i-\overline{prof})^2\ p(prof_i)

$

$\displaystyle

=(375-900-225)^2 0.1+(2\times375-900-225)^2 0.2+$$\displaystyle (3\times375-900-225)^2 0.3+(4\times375-900-225)^2 0.4

$

$\displaystyle

=140625

$

b) Find the standard deviation in profit each week.

Standard deviation is the square root of variance and so:

$\displaystyle

\sigma=\sqrt{140625}=\$375

$

RonL