This post is a follow up for my previous Classroom Blogging Activity post. This outlines an example of what I would like to see as a product from my students.

### Standard III.A.4

SWBAT use a probability distribution to answer questions about possible values of a random variable.

Courtesy of the College Board AP Statistics Course Description

### Example

The heights of young women closely follow the Normal distribution with mean mu=64 inches and standard deviation sigma=2.7 inches. The is a distribution for a large set of data. Now choose one young woman at random. Call her height Y. If we repeat the random choice very many times, the distribution of values of Y is the same Normal distribution that describes the heights of all young women. Find the probability that the chosen woman is between 68 and 70 inches tall.

Example Courtesy of AP Statistics by Starnes

### Mathematical Solution and Written Explanation

The height Y of the woman we choose has the N(64, 2.7) distribution. We want to find P(68<Y<70). This is the area under the Normal curve between the standardized z-values that correspond with 68 and 70 inches as shown in the picture below.

Picture Courtesy of AP Statistics by Starnes

Find the z-values that correspond to 68 and 70 inches…

z=(68-64)/2.7=1.48

z=(70-64)/2.7=2.22

Using table A these z-values give probabilities below 1.48 and 2.22 of .9306 and .9868 respectively.

Table Courtesy of PBWorks

Therefore the probability between the values is .9868 – .9306 = .0562 or 5.62%.

Conclusion: There is about a 5.6% chance that a randomly chosen young woman has a height between 68 and 70 inches.

### Conclusion of EdTech 537

Signing off of EdTech 537 – Angie Kruzich

Thanks for posting an example Angie! It really helps your lesson “come to life”!

Have a great school year.

Hi Kim: Good, I’m glad you like the example. Hopefully it is an excellent demo of what I expect from the students!! – Angie

Angie,

The images really have an impact.Good luck, it looks like your students will be doing some serious work đŸ™‚

And thank goodness for google images…they are a life saver when writing examples on the computer!! – Angie