# Normal distributions

#### jerttehcamper

##### New Member
I have been using my TI 84 Plus Silver Edition calculator to try and figure this out with no luck :-( Can anyone help?

Assume that the heights of women are normally distributed with a mean of 63.6 inches and std. dev of 2.5. To be eligible for the US Army, a woman's height must be between 58 and 89 inches. If the requirement is changed, find the minimum acceptable heights so that only shortest 1% will be excluded from being accepted in the Army.

A. 56.66
B. 57.78
C. 61.42
D. 69.42

Find maximum acceptable heights so that only talest 1% will be excluded from being accepted in Army.

A. 56.66
B. 57.78
C. 61.42
D. 69.42

#### Dason

##### Ambassador to the humans
What work have you done so far? Elaborate on what you've tried so far and what you think you need to do.

#### jerttehcamper

##### New Member
Well the issue is that I don't even know where to begin...if I did I might actually be able to solve the problem...if you are unable to help, that's fine.

#### Dason

##### Ambassador to the humans
It's not that I don't know what to do. I and almost everybody else on the board know how to do this problem. We do not, however, just give out answers without some sort of evidence of effort or work.

This thread explains that policy.

All I'm asking for is for you to explain what you know how to do and which parts are giving you trouble. You say you don't even know where to start. That's fine. But tell me what you've been learning recently in the class and how that might relate to the problem.

##### Ninja say what!?!
I'd say that when in doubt, choose C. Don't think that's the right answer here though. Good luck!

#### jerttehcamper

##### New Member
I understand and respect your policy completely. I am an RN taking this class online because I have to in order to get a higher degree. I have been taking it online as that is all I have time for. Perhaps that's why I do not understand this particular material. I have been learning recently how normal distributions are always symetrical about the mean and have a bell shape. I also know their are infinitely many normal distributions for random var x. I also know how to convert x values to their corresponding z scores by subtracting the mean from x and then dividing by the std. dev. With all that said, the information given in this problem are doing nothing for me in terms of how to plug them in to the calculator.

#### Mean Joe

##### TS Contributor
It's comforting to know that the US Army allows women up to 89 inches tall.

A couple things:
1) To use your calculator: You know how to access the NORMALCDF( ... ) function? Press [2nd] [VARS], and it's under DISTR. Or something like that; your version of the TI may differ. This is the first thing that came up in Google
I'm not familiar with working on these new calculators (I'm an oldz). If you really want to go this way, I'd have to guess and check with the offered answers. eg normalcdf(56.66, 10^100, 63.6, 2.5) [enter] and see if that gets you .01

2) Remember the rule of thumb: 66% of samples within 1 s.d., 95% of samples within 2 sd, and 99% of samples within 3 sd. Although this applies to two tails (your question pertains to 1 tail, as it talks about excluding only the 1% lowest, rather than 1% lowest and highest). But it's a quick check to get an idea of what to guess.

3) Your second question, the answer is obvious. Only one choice is above the mean.