Question 1203241: Please show me how to solve this problem. Thanks!
In order to be accepted into a ROTC Program, applicants must score within the top 5% on the Military Admission Test. Given that this test has a mean of 1,600 and a standard deviation of 150, what is the lowest possible score a student needs to qualify for acceptance into the ROTC Program?
The lowest possible score is:
(Round your answer to the nearest whole number.)
Answer by ikleyn(52887)   (Show Source):
You can put this solution on YOUR website! .
Please show me how to solve this problem. Thanks!
In order to be accepted into a ROTC Program, applicants must score within the top 5%
on the Military Admission Test. Given that this test has a mean of 1,600
and a standard deviation of 150, what is the lowest possible score a student needs
to qualify for acceptance into the ROTC Program?
The lowest possible score is:
(Round your answer to the nearest whole number.)
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You can solve it, using your regular calculator TI83 or TI84.
The normal curve is a bell-shaped curve.
They want you find z-score for the specified normal curve in a way that the area under
this normal curve be 0.05 on the right of this z-score, or, which is the same,
the area be 0.95 on the left on that z-score.
Use the standard function invNorm of the calculator
area mean SD <<<---=== formatting pattern
z = invNorm(0.95, 1600, 150)
You get z-score value z= 1846.728.
We use the area value 0.95, since the function's invNorm first argument is the area on the left of z-score.
To be consistent with the question, you should round it
to the nearest GREATER whole number, so your ANSWER is 1847.
It is the lowest possible integer score.
Solved.
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Another way to get the answer is to use this online free of charge calculator
https://davidmlane.com/hyperstat/z_table.html
It has very convenient interface, so even beginner student can easily use it.
The calculator shows the area under the normal curve, for which you look for z-score,
so you may understand the process.
This calculator is a first class teacher. Use it to quickly learn the subject.
Surely, using the online calculator, you will get the same answer.
When you use this online calculator, be sure to use option "Value from an area" of two possible options.
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If you need instructions on how to get function invNorm in TI83-TI84
and how to work with it, you may find such instructions in this web-page
https://www.statology.org/invnorm-ti-84/
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