Recentering Normal Curves, revisited

I wrote here about using a CAS to determine a the new mean of a recentered normal curve from an AP Statistics exam question from the last decade.  My initial post shared my ideas on using CAS technology to determine the new center.  After hearing some of my students’ attempts to solve the problem, I believe they took a simpler, more intuitive approach than I had proposed.

REVISITING:

In the first part of the problem, solvers found the mean and standard deviation of the wait time of one train: \mu = 30 and \sigma = \sqrt{500}, respectively.  Then, students computed the probability of waiting to be 0.910144.

normCAS1

The final part of the question asked how long that train would have to be delayed to make that wait time 0.01.  Here’s where my solution diverged from my students’ approach.  Being comfortable with transformations, I thought of the solution as the original time less some unknown delay which was easily solved on our CAS.

normCAS4

STUDENT VARIATION:

Instead of thinking of the delay–the explicit goal of the AP question–my students  sought the new starting time.  Now that I’ve thought more about it, knowing the new time when the train will leave does seem like a more natural question and avoids the more awkward expression I used for the center.

The setup is the same, but now the new unknown variable, the center of the translated normal curve, is newtime.  Using their CAS solve command, they found

newnorm

It was a little different to think about negative time, but they found the difference between the new time difference (-52.0187 minutes) and the original (30 minutes) to be 82.0187 minutes, the same solution I discovered using transformations.

CONCLUSION:

This is nothing revolutionary, but my students’ thought processes were cleaner than mine.  And fresh thinking is always worth celebrating.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s