SOLUTION: x P(x)
0 0.05
1 0.2
2 0.15
3 0.6
Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places.
I have attempted to mu
Algebra ->
Probability-and-statistics
-> SOLUTION: x P(x)
0 0.05
1 0.2
2 0.15
3 0.6
Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places.
I have attempted to mu
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Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places.
I have attempted to multiply each x value by its corresponding P(x) value, and then added those values together. I got 1.97 as an answer, and it was incorrect. Found 2 solutions by ikleyn, math_tutor2020:Answer by ikleyn(52803) (Show Source):
The sum of the x*p(x) values is the mean.
Refer to the table below to see that the mean should be mu = 2.3 instead of 1.97
x
p(x)
x*p(x)
(x-mu)^2*p(x)
0
0.05
0
0.2645
1
0.2
0.2
0.338
2
0.15
0.3
0.0135
3
0.6
1.8
0.294
Sum
1
2.3
0.91
That value of mu is then used to calculate the column (x-mu)^2*p(x)
The sum of those values is 0.91 which is the variance. This value is exact without any rounding done to it.
Apply the square root of the variance to get the standard deviation.
SD = standard deviation
SD = sqrt(variance)
SD = sqrt(0.91)
SD = 0.953939 approximately
SD = 0.95
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