Suppose the age of people in a certain population are distributed normally with a mean of 37.5 years and standard deviation of 6.2 years. What is the probability of randomly selecting a person who is over 45 years old given that they are older than 40.

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:

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step-by-step explanation:

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