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Question

based on market research :

if the sales of a product are high
the company can make a profit of $3.1million/year
if 'so so', make a profit of $1.5million/year
if sales are low then lose $0.5million

the probabilities for the two profit scenarios are 0.65 and 0.14 respectively

calculate the standart deviation of profit for the prodcut in millions to 3 decimal places

too hard to put the standard deviation formular here
my answer is
[0.65-(0.65+0.14)/n]square/n-1=
if the n is =2
then =0.065025
open root =0.255

does it seem right to you?

repects for y'all who check this answer for me.
thx a lot.

hello,more answers?

Answer 1

Well, here's an easy way. Without looking it up, my favorite S.D. formula is (1/n) sqrt(n sumsq - sumx^2) where sumsq is the sum of the x^2 data, and sumx is just the sum of the x data. We don't have to worry about sample size because you have established probabilities.

With your data, suppose we looked at a hundred years of data. We'd have high profits 65 times, "so-so" profits 14 times, and a loss 21 times. n = 100.

I just typed that into my calculator and got this: mean profit $2.12 million; S.D. $1.463 million (sample); S.D. $1.456 million (population); sumx = 212 (million); sumsq = 661.4

So the mean profit is $2.12 million with a standard deviation of $1.456 million. If this data were normally distributed (which it's not), we'd estimate that profit would be between $657,000 and $3.569 million 68% of the time.

Answer 2

Is any one out there with an IQ of 160 or more?

Answer 3

You need to calculate expected values to find the variance first.

Var(x)=E(x^2)-E(x)^2

E(x^2)=(3,100,000^2)*.65+
(1,500,000^2)*.14+
(-500,000^2)*(1-.65-.14)

E(x)=(3,100,000)*.65+
(1,500,000)*.14
-500,000*(1-.65-.14)

stand dev=(Var(x))^.5