Answer:
a)
b)
And using a calculator, excel or the normal standard table we have that:
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
Part a
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
Where
and
Since the distribution for X is normal then we know that the distribution for the sample mean
is given by:
Part b
We want to find this probability:
![P(\bar X >124)](https://tex.z-dn.net/?f=%20P%28%5Cbar%20X%20%3E124%29)
And we can use the z score given by:
![z = \frac{\bar X -\mu}{\sigma_{\bar X}}](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B%5Cbar%20X%20-%5Cmu%7D%7B%5Csigma_%7B%5Cbar%20X%7D%7D)
And using this formula we got:
And using a calculator, excel or the normal standard table we have that: