Respuesta :
Answer: The mean of daily sales is $8,333.33 and the standard deviation of daily sales $19,507.83.
We arrive at the answer as follows:
1. Obtaining probability distribution for daily sales
On any day, the number of sales may be either 0 ,1 or 2.
We compute each of the probabilities as:
[tex]P(X=0) = P(1 customer and no sales) + P( 2 customers and no sales)[/tex]
[tex]P(X=0) = (\frac{1}{3}*0.9) + (\frac{2}{3}* [0.9*0.9])[/tex]
[tex]\mathbf{P(X=0) = 0.84}[/tex]
[tex]P(X=1) = P(1 customer and 1 sale) + P( 1st customer and sales + 2nd customer and no sales) + P( 1 customers and no sales + 2nd customers and sales)[/tex]
[tex]P(X=1) = (\frac{1}{3}*0.1) + (\frac{2}{3}*\frac{1}{10}*\frac{9}{10}) + (\frac{2}{3}*\frac{9}{10}*\frac{1}{10})[/tex]
[tex]\mathbf{P(X=1) = 0.153333333}[/tex]
Since we know the P(X=0) and P(X=1), we can calculate P(X=2) as:
[tex]P(X=2) = 1 - P(X=0)- P(X=1)[/tex]
[tex]P(X=2) = 1 - 0.84 - 0.153333333[/tex]
[tex]\mathbf{P(X=2) = 0.006666667}[/tex]
Now that we have the Probability distribution of daily sales, we can compute the mean of daily sales as follows:
Let V be value of sales per day, the mean is
Daily Sales P Value of sales -v v*P
0 0.8400 0 0
1 0.1533 50000 7666.666667
2 0.0067 100000 666.666667
Total 1 8333.333333
The total in the table above is the mean of daily sales.
We calculate Standard Deviation as
[tex]\sigma = \sqrt{[(0 - 8333.3333)^{2})*0.84] + [(7666.666667 - 8333.3333)^{2})*0.1533]+[(666.666667 - 8333.3333)^{2})* 0.0067]}\\[/tex]
[tex]\mathbf{\sigma = 19507.83318}\\[/tex]
