A normal distribution has a mean of μ = 100 with LaTeX: \sigmaσ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 100 and X = 130?

And we can find this probability with this difference:

And in order to find these probabilities we can using tables for the normal standard distribution, excel or a calculator.  

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 variable of interest 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 with this difference:

And in order to find these probabilities we can using tables for the normal standard distribution, excel or a calculator.  

just pick what you think i need more time let me know if this

step-by-step explanation: