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Sagot :
The correct interpretation of the standard deviation of the given discrete distribution is:
The mean number of days a member worked out would typically be about 1.6764 from the expected number of days.
What are the mean and the standard deviation of a discrete distribution?
- The mean of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
- The standard deviation is the square root of the sum of the difference squared between each outcome and the mean, multiplied by it's respective probabilities.
Hence:
E(X) = 0.4(0) + 0.12(1) + 0.13(2) + 0.15(3) + 0.06(4) + 0.02(5) + 0.02(6) + 0.01(7) = 1.36
[tex]\sqrt{V(X)} = \sqrt{0.4(0-1.36)^2 + 0.12(1-1.36)^2 + 0.13(2-1.36)^2 + \cdots + 0.01(7-1.36)^2} = 1.674[/tex]
Hence the correct option is:
The mean number of days a member worked out would typically be about 1.6764 from the expected number of days.
More can be learned about discrete distributions at https://brainly.com/question/24855677
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