Question

A foundation repair contractor promises to provide a free quote to any potential customer who requests it. A quote costs him $ 40 (in inspection and preparation time) but only results in a contract 25% of the time. A contract, however, earns him an average of $ 250 net (after deducting the cost of the quote). In order to properly measure the financial risk on his business, the entrepreneur wants to know what a bad day may look like after receiving 20 quotes on a single day. It then defines P, the worst realistic scenario, as the expectation of total net gains minus one standard deviation. Determine the value of P.

thanks for your help

Answer 1

Cost of quote = $40

So, amount lost if he does not recieve contract =$40

Earnings per contract = $250

Prabability of contract = 0.25 (or 25%)

Prabability of no contract = 0.75 (or 75%)

Event	Payoff (profit) = X	probability =p(x)
Contract	$250	0.25
No contract	-$40	0.75

Mean = = 250*0.25 + (-40)*0.75 =$32.5

Standard deviation ()

=$108.94

So, For one quote,

Expected total net gains minus one standard deviation = 32.5 - 108.94

=$76.44

For 20 quotes,

Expected total net gains minus one standard deviation =20*76.44

=20*(-76.44)

=-$1528.8

Thus, on a bad day he will lose $1528.8 after receiving 20 quotes.