# Range of Data Values That Includes 95% of my Data

For a math assignment, I am required to find the range of data values that would include 95% of my data.

My data is the wait time for a specific bus. I have gathered 20 pieces of data for this, where each number represents how late(+)/early(-)/on time(0) the bus is.

This is the organized data in ascending order: 0, 1, -4, 0, -3, 0, -4, -2, 0, 1, -1, 2, 0, -4, 5, -2, 0, 3, -3, 0.

The link attached down below is my normal distribution graph where I have listed the mean (-0.55), standard deviation(2.4), and the graph information.

What I think the range would be is (-5) - 4. I came to this conclusion by looking at the normal distribution graph above. Although I`m concerned about my answer.

If this data is normally distributed with $$\mu=-0.55$$ and $$\sigma=2.4$$ we can say that X, the wait time for a specific bus, is distributed as follows: $$X\sim N(-0.55,(2.4)^2)$$ For 95% of the data to be included we want $$P(\mu-a. As the normal distribution is symmetrical we can simplify this to finding: $$P(X>\mu+a)=\frac{1-0.95}{2}=0.025$$ or similarly $$P(X<\mu-a)=0.025$$. Using the Inverse Normal function (a website can be found here to do this) we find that $$\mu-a=-5.2539$$, such that: $$a=\mu+5.2539=-0.55+5.2539=4.7039$$ The range of data required is then $$2\cdot a =2\cdot(4.7039)= 9.407$$8 as the data ranges from $$\mu-a$$ to $$\mu+a$$.