A survey found that women’s heights are normally distributed with mean 63.5 in and standard deviation 2.5 in. A branch of the military requires women’s heights to be between 58in and 80 in. since the height requirements have changed to a percentage of 0.986% What would then be the new height requirements?

- anonymous

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- amistre64

it sounds like its asking for an interval
but this part is hard to understand:
"since the height requirements have changed to a percentage of 0.986%"

- anonymous

Oh well maybe I needed to make that decimal into a percentage...

- anonymous

98.6% oops

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## More answers

- amistre64

but what does the information mean? i cant make sense of what it is asking of us

- amistre64

does it mean that we want to find an 98.6% interval?

- anonymous

A survey found that women’s heights are normally distributed with mean 63.5 in and standard deviation 2.5 in. A branch of the military requires women’s heights to be between 58in and 80 in.
b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?

- amistre64

that one reads better

- anonymous

Sorry :/

- amistre64

we are given percentages (areas), and need to find the z score related to them
what function takes an area, and gives us a zscore?

- anonymous

2nd vars

- anonymous

or stats?

- amistre64

2nd vars is a button combination, which takes us to a distribution menu.

- amistre64

press it and see what we get for function options ...

- anonymous

id say the 3rd for invnorm

- amistre64

invnorm takes an area, and gives a zvalue. good
what is the zvalue for 1%? invnorm(.01)
what is the zvalue for 2%? invnorm(.02)

- anonymous

So Id then put in my new percentage and input (0.1) and (0.2)

- amistre64

work it 2 times ... use .01 and .02

- amistre64

.10 is 10%; .01 is 1%

- anonymous

So invnorm(98.6, .01,.02)

- anonymous

or (98.6,1,2)

- amistre64

no, its exactly like a wrote above
invnorm(.01)

- anonymous

-2.326

- amistre64

and invnorm(.02) is?

- anonymous

-2.053

- anonymous

Would I then take out the negative? Also, would I make them a percentage or leave as a decimal?

- anonymous

Ok, leave as decimal. I just read that

- amistre64

now comes some mental gymnastics ... this gave us the bottom 1% and bottom 2%
bottom 1% is fine, its what we want
TOP 2% is what we desire, the good news is, the top is just the opposite of the bottom
TOP 2% = 2.053
--------------------
our interval is therefore the calculations of:
63.5 -2.326(2.5)
63.5 +2.053(2.5)

- anonymous

So the top should be rounded to 2.33?

- anonymous

for the 1%

- amistre64

no, i mentioned nothing about rounding.

- anonymous

Oh ok so leave as is

- amistre64

what is: 63.5 -2.326(2.5)
and what is: 63.5 +2.053(2.5)

- anonymous

2.326 and 2.053

- amistre64

those are z values, we use them to define the interval with ..

- anonymous

invnormcdf?

- anonymous

normalcdf***

- amistre64

of course not ... you have to work out the actual calculations now, and im only going to post this this last time ...
what is: 63.5 -2.326(2.5)
and what is: 63.5 +2.053(2.5)

- anonymous

-.9999 for the first

- amistre64

when you get around to answering my question, let me know ...

- anonymous

and -1.4321 for the second

- amistre64

no, we are not using any functions now, we are doing elementary school math ... addition and multiplication.

- anonymous

I know. I was using the normalcdf. I thought that is what I needed to use..

- amistre64

no, we simply need to use this
63.5 -2.326(2.5)

- anonymous

57.685

- anonymous

for the first

- anonymous

68.6325 for the second

- anonymous

Sorry about the confusion

- amistre64

i never made any mention of, nor gave reference to, any other function other than the invnorm ... and that was to determine some z values which we can then use to define our interval with
57.6850 is good for the low end
68.6325 is good for the high end

- anonymous

Thank you again for your help. I really do appreciate it.

- amistre64

your welcome

- anonymous

Math is just my absolute worst subject! Any form of medical term I can understand but this stuff is horrible!

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