The correct interpretation of the standard deviation of the discrete distribution is:
- The number of eggs laid on a randomly selected day would typically vary from the expected number of eggs by 1.4 eggs.
What is the standard deviation of a discrete distribution?
- To find the standard deviation, first we have to find the mean.
- The mean is given by the sum of each outcome multiplied by it's respective probability.
- The standard deviation is given by the square root of the sum of the difference squared of each outcome and the mean, multiplied by it's respective probability.
- It represents by how much the distribution varies from the expected value.
In this problem, the distribution is:
[tex]P(X = 0) = 0.02[/tex]
[tex]P(X = 1) = 0.03[/tex]
[tex]P(X = 2) = 0.07[/tex]
[tex]P(X = 3) = 0.12[/tex]
[tex]P(X = 4) = 0.30[/tex]
[tex]P(X = 5) = 0.28[/tex]
[tex]P(X = 6) = 0.18[/tex]
Hence, the mean is:
[tex]E(X) = 0.02(0) + 0.03(1) + 0.07(2) + 0.12(3) + 0.3(4) + 0.28(5) + 0.18(6) = 4.21[/tex]
Then, the standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{0.02(0-4.21)^2 + 0.03(1-4.21)^2 + 0.07(2-4.21)^2 + 0.12(3-4.21)^2 + 0.3(4-4.21)^2 + 0.28(5-4.21)^2 + 0.18(6-4.21)^2} = 1.40[/tex]
Hence, the correct option is:
- The number of eggs laid on a randomly selected day would typically vary from the expected number of eggs by 1.4 eggs.
As the measure is the number of eggs, not the mean number of eggs.
You can learn more about the standard deviation of a discrete distribution at brainly.com/question/21186607
