If outliers are discarded, then the retirement savings by residents of Econistan is normally distributed with a mean of $100,000 and a standard deviation of $20,000. a) What is the probability that one randomly selected resident of Econistan will have retirement savings greater than $117,000? Please include a picture and calculations in your answer.

And we can find this probability using the complement rule and the normal standard table or excel:

The firgure attached illustrate the problem

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 retirement savings of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using the complement rule and the normal standard table or excel:

The firgure attached illustrate the problem

a² + b²= c²

24² + 7² = c²

c= 25