Answer:
The mean is given by:
![\mu_{\bar X}= 1.3](https://tex.z-dn.net/?f=%5Cmu_%7B%5Cbar%20X%7D%3D%201.3)
And the deviation is given by:
![\sigma_{\bar X} =\frac{\sigma}{\sqrt{n}}= \frac{1.4}{\sqrt{30}}= 0.256](https://tex.z-dn.net/?f=%5Csigma_%7B%5Cbar%20X%7D%20%3D%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%3D%20%5Cfrac%7B1.4%7D%7B%5Csqrt%7B30%7D%7D%3D%200.256)
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the number of siblings of a population, and for this case we know the distribution for X is given by:
Where
and
The sample mean is given by this formula:
![\bar X = \frac{\sum_{i=1}^n X_i}{n}](https://tex.z-dn.net/?f=%5Cbar%20X%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20X_i%7D%7Bn%7D)
The sample size is n =30, and the distribution for the sample mean is given by:
The mean is given by:
![\mu_{\bar X}= 1.3](https://tex.z-dn.net/?f=%5Cmu_%7B%5Cbar%20X%7D%3D%201.3)
And the deviation is given by:
![\sigma_{\bar X} =\frac{\sigma}{\sqrt{n}}= \frac{1.4}{\sqrt{30}}= 0.256](https://tex.z-dn.net/?f=%5Csigma_%7B%5Cbar%20X%7D%20%3D%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%3D%20%5Cfrac%7B1.4%7D%7B%5Csqrt%7B30%7D%7D%3D%200.256)