A popular streaming service surveyed all of the students at a school about the number of TV shows they streamed
last Friday night, then recorded the results.
Let M = the number of TV shows streamed last Friday night.
Number of Shows Streamed 0
1
2
3
4.
5
Probability
0.095
0.203
0.326
0.187
0.174
0.015
Calculate the standard deviation of M.
1.251 shows
1.566 shows
1.708 shows
2.917 shows

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joaobezerra joaobezerra · Answer 1 · 2022-01-24T11:31:32+01:00

Using the given discrete distribution, it is found that the standard deviation is of 1.251 shows.

The mean is given by the sum of the multiplications of each outcome by it's probability, thus:

The standard deviation is given by the square root of the sum of the squares of each outcome subtracted by the mean, multiplied by it's probability, thus:

The distribution is:

[tex]P(X = 0) = 0.095[/tex]

[tex]P(X = 1) = 0.203[/tex]

[tex]P(X = 2) = 0.326[/tex]

[tex]P(X = 3) = 0.187[/tex]

[tex]P(X = 4) = 0.174[/tex]

[tex]P(X = 5) = 0.015[/tex]

Hence, the mean is:

[tex]E(X) = 0.095(0) + 0.203(1) + 0.326(2) + 0.187(3) + 0.174(4) + 0.015(5) = 2.187[/tex]

The standard deviation is:

[tex]\sqrt{V(X)} = \sqrt{0.095(0-2.187)^2+0.203(1-2.187)^2+0.326(2-2.187)^2+0.187(3-2.187)^2+0.174(4-2.187)^2+0.015(5-2.187)^2} = 1.251[/tex]

You can learn more about the mean and the standard deviation of a discrete distribution at https://brainly.com/question/13008984