Answer:
By definition
since in a continuous probability distribution the area below a line is 0
If the real question is:
![P(X](https://tex.z-dn.net/?f=%20P%28X%3C6076%29)
We can use the z score formula given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel:
And if the question is
we apply the complement rule and we got:
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 strengths of a population, and for this case we know the distribution for X is given by:
Where
and
For this case we want ![P(X= 6076)](https://tex.z-dn.net/?f=%20P%28X%3D%206076%29%20)
And by definition
since in a continuous probability distribution the area below a line is 0
If the real question is:
![P(X](https://tex.z-dn.net/?f=%20P%28X%3C6076%29)
We can use the z score formula given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel:
And if the question is
we apply the complement rule and we got: