Stat List Editor on Ti-89 for finding areas between z-scores

Hello,

I've been having some trouble with my Stat List Editor application on the TI-89 Titanium (well, more like (Headbang) than just a normal problem). I can't seem to get the correct answer for a statistics problem, no matter what field I put my numbers in (I'm also pretty clueless about SLE in general, since my professor doesn't know how to use an 89, and can't help me in class).

Here's the problem:

Find the z-score for which 5% of the distribution's area lies between -z and z.

For a similar problem (with 80% instead of 5%), I got the right answer by looking at the Critical Values list on my z-score chart. I looked under .80 in the 'level of confidence column,' and then looked to its corresponding z_c column, to get 1.28 and -1.28 as my answers. Unfortunately, this list only starts at .80, and only gives the z_c for .9, .95, and .99.

Would anyone know to solve the problem above, and others like it, with SLE, by hand, or otherwise?

Look for z values of p=2.5% or p=97.5% on 2-sided normal distribution table and you might need to interpolate between 97.5% and 95% or 99%. Be careful your z values might be for 1-sided probability table but you need 2.5% each side of mean. $\displaystyle z_{0.975}=1.95$

Alternately, for the first problem you could enter the command on your TI-89:

solve(1/√(2π)∫(e^(-x^2/2),x,0,z)=.025,z) [ENTER]

result: .062706777943

Now, instead of 5%, if you try this with 80% you would enter:

solve(1/√(2π)∫(e^(-x^2/2),x,0,z)=.4,z) [ENTER]

result: 1.28155156554

Thanks for your help, guys!

I still have a few questions...

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Alternately, for the first problem you could enter the command on your TI-89:

solve(1/√(2π)∫(e^(-x^2/2),x,0,z)=.025,z) [ENTER]

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Mark, would it be possible to save this equation into a single command (i.e. making it so I only had to press 1 button, and the equation would come up, instead of typing the whole thing out each time)?

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Look for z values of p=2.5% or p=97.5% on 2-sided normal distribution table and you might need to interpolate between 97.5% and 95% or 99%. Be careful your z values might be for 1-sided probability table but you need 2.5% each side of mean.

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Max, why would you look at 2.5 or 97.5? Do you have to add/subtract 2.5 each time from the needed percentage in this case, or this a universal rule?

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Originally Posted by m58

Max, why would you look at 2.5 or 97.5? Do you have to add/subtract 2.5 each time from the needed percentage in this case, or this a universal rule?

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Your original problem is:
"Find the z-score for which 5% of the distribution's area lies between -z and z."

Correction:

-z to +z indicates that 5% is considered from -z to +z which means 47.5% each side of the mean,i.e., 47.5% for values less than -z and 47.5% for values greater than +z. as indicated on the N-Dist graph:

$\displaystyle z=\pm 0.062707$ for blue area=2.5%

https://encrypted-tbn1.gstatic.com/i...M2XwwTnAfgUv0A

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Originally Posted by MaxJasper

Your original problem is:
"Find the z-score for which 5% of the distribution's area lies between -z and z."


-z to +z indicates that 100%-5% =95% is considered from -z to +z which means 2.5% each side of the mean,i.e., 2.5% for values less than -z and 2.5% for values greater than +z. as indicated on the N-Dist graph:

http://img.tfd.com/mk/D/X2604-D-41.png

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Got it! Thanks for your help.

Please see corrections.

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Originally Posted by m58

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Mark, would it be possible to save this equation into a single command (i.e. making it so I only had to press 1 button, and the equation would come up, instead of typing the whole thing out each time)?

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You could try saving the command as a script, but I haven't used this function.

The solve command is available on the algebra menu (F2) and the integrate function is available on the calculus menu (F3).