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

Question 1199130: 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 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): You can put this solution on YOUR website!
.

Go to web-site

https://www.calculator.net/standard-deviation-calculator.html?numberinputs=0.05+0.2+0.15+0.6&ctype=p&x=41&y=20

and use free of charge online calculator there.

In parallel, learn the theory/formula from this web-page.

The answer is 0.209165, and you can round it as you want.

If you need instructions on how to do it using TI-83 or TI-84, see and learn from these websites

https://www.youtube.com/watch?v=DdQHwgAVePk
(youtube video-lesson)

https://www.mathbootcamps.com/how-to-find-the-standard-deviation-and-variance-with-a-graphing-calculator-ti83-or-ti84/
(textual description)

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

You made an error somewhere when calculating the 1.97

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

Various online calculators can be used to verify this result.
Here is one such calculator
https://www.mathportal.org/calculators/statistics-calculator/probability-distributions-calculator.php

More practice with a similar question
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1206570.html

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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