Answer:
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 age of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability:
We can begin finding using the z score formula given by:
Using this formula we have:
And using the complement rule and the normal standard table or excel we have this:
Now we can find using the z score formula given by:
Using this formula we have:
And using the complement rule and the normal standard table or excel we have this:
And replacing into our original probability we got: