Ok this unit is on z scores and find area of shaded region blah blah. This stupid stat lab thing just keeps saying use technology to find the answer. I've tried excel the exact way it tells me and the answer is never right. Can someone explain to me wtf is going on here?


Example, the question I am on:

A survey found that​ women's heights are normally distributed with mean
63.6in and standard deviation 2.5in. A branch of the military requires​ women's heights to be between 58 in and 80 in.
a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too​ tall?
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?


a. The percentage of women who meet the height requirement is

This post was edited by sbc'soneandonly on Mar 3 2016 10:54am

First let's estimate an answer from common sense that we can use the check the sanity of our answer.

58 inches is 4'10"
80 inches is 6'8"

Pretty much every woman I've ever met falls within those limits so I estimate that the answer is less than 0.01 (less than 1%).
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Now calculate how many standard devs the right hand side (80 inches) is from the mean, look it up on a z table (http://www2.parkland.edu/businesstraining/documents/zscoretable.pdf), and write down that number (I'll call it A).

Do the same for the left hand side (58 inches) and call it B.

The answer is (A-B)*100. It is *100 because they ask for the percentage.

As a sidenote, the 80 inches is so many standard devs away from the mean that you probably will not find it on the table. You can see that the table approaches the value of 1 in that direction so just use 1.
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For the second part you want to do the opposite. Go to the table an look up 0.01 and see how many standard devs that is, then figure out how many inches that is (this is the cut off for the shortest 1%), then repeat that for 98% (cut off to exclude tallest 2%).

Sorry I just realized by initial estimate was for how many would be excluded, not included. So change my estimate to 1 - 0.01 = 0.99 or 99%

Ok now what about when this damn mathlab tells me, and I quote, "use technology to find...". What kind of shit is that? Like it says to use T instead of Z if there is no standard deviation or the sample is over 30. But one of the examples has them using T for a sample of 8 with the standard deviation given. It makes no sense.

If you know the standard dev, use normal distribution (Z)

If you don't know the stand dev:
if you have 30+ samples, use normal distribution (Z)
if you have 29 or less samples, use one of the t-distributions (T)

When they refer to 'use technology' they just mean use some kind of technical aid to help you get the score. Like an advanced calculator(like a TI), math program ( perhaps Mathlab) , or spreadsheet program(perhaps excel). These all have functions you can use to get the results.