How is inductive reasoning used in geometry?

Because our conclusion is based on facts, the conclusions reached by deductive reasoning are correct and valid. Simply put, inductive reasoning is used to form hypotheses, while deductive reasoning is used more extensively in geometry to prove ideas.

And using a calculator, excel ir the normal standard table we have that:

TRUE.

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

Since S follows a normal distribution then we know that the distribution for the sample mean is given by:

We can find the probability of interest with the following expression:

And using a calculator, excel ir the normal standard table we have that:

TRUE.