Question 1196800
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<font color=red>Answers:</font> 
Mean = 1.84
Standard Deviation = 0.997


The mean is exact, while the standard deviation is approximate. 


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Work Shown: 


We'll use this table to compute the mean
<table border = "1" cellpadding = "5"><tr><td>x</td><td>0</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>Total</td></tr><tr><td>P(x)</td><td>0.03</td><td>0.42</td><td>0.3</td><td>0.19</td><td>0.05</td><td>0.01</td><td>1</td></tr><tr><td>x*P(x)</td><td>0</td><td>0.42</td><td>0.6</td><td>0.57</td><td>0.2</td><td>0.05</td><td>1.84</td></tr></table>
The x*P(x) row refers to multiplying each column of x and P(x) values. 
Then we add up all of the x*P(x) values to get 1.84 which is the mean.


The Greek letter mu is often used as the mean
So we have mu = 1.84 and this value is useful to find the standard deviation.
<table border = "1" cellpadding = "5"><tr><td>x</td><td>0</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>Total</td></tr><tr><td>P(x)</td><td>0.03</td><td>0.42</td><td>0.3</td><td>0.19</td><td>0.05</td><td>0.01</td><td>1</td></tr><tr><td>X-mu</td><td>-1.84</td><td>-0.84</td><td>0.16</td><td>1.16</td><td>2.16</td><td>3.16</td><td></td></tr><tr><td>(x-mu)^2</td><td>3.3856</td><td>0.7056</td><td>0.0256</td><td>1.3456</td><td>4.6656</td><td>9.9856</td><td></td></tr><tr><td>(x-mu)^2*P(x)</td><td>0.101568</td><td>0.296352</td><td>0.00768</td><td>0.255664</td><td>0.23328</td><td>0.099856</td><td>0.9944</td></tr></table>
The value 0.9944 in the bottom right corner represents the sum of the (x-mu)^2*P(x) values
This value also represents the variance of the probability distribution table.


Take the square root of the variance to get the standard deviation
standard deviation = sqrt(variance)
standard deviation = sqrt(0.9944)
standard deviation = 0.99719606898543
standard deviation = 0.997
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