Question 1197675: The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, where the amount requested for home loans followed the normal distribution with a mean of $80 000 and a standard deviation of $24 000. (Round z-score computation to 2 decimal places and the final answers to the nearest whole dollars.)
a. What is the minimum amount requested on the largest 2% of loans?
$
b. What is the maximum amount requested on the smallest 10% of loans?
$
Found 2 solutions by ikleyn, ewatrrr:
Answer by ikleyn(52798)   (Show Source):
You can put this solution on YOUR website! .
The amounts of money requested on home loan applications at Down River Federal Savings
follow the normal distribution, where the amount requested for home loans followed
the normal distribution with a mean of $80 000 and a standard deviation of $24 000.
a. What is the minimum amount requested on the largest 2% of loans?
b. What is the maximum amount requested on the smallest 10% of loans?
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(a) The normal distribution is a bell-shaped curve.
In this question, you are given the area under the specified normal distribution curve
on the right of the row z-score of 1-0.02 = 0.98.
It means that they want you find the value of the inverse accumulated normal distribution function
at the mean value of 80,000, standard deviation of 24,000, and the row z-score of 0.98.
You may use online free of charge calculator
https://onlinestatbook.com/2/calculators/inverse_normal_dist.html
It will show you the entire process in visual form,
so you will see and understand what you are doing and you will be able to learn.
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| Using this online calculator is indispensable as a teaching tool |
| for a beginner student to learn the subject. |
+---------------------------------------------------------------------+
Alternatively, if you just have some introductory conceptual knowledge, you can use your standard calculator.
The function to use is invNorm(mean,SD,z).
If you need instructions for it, you can find them in the internet at this link
https://www.youtube.com/watch?v=RPzxs-Hd8s0 (video-lesson for Casio calculators) or
https://www.youtube.com/watch?v=7mkfGJO8ehM (video-lesson for TI-83 or TI-84) or
https://cosmosweb.champlain.edu/people/stevens/WebTech/TIFiles/Chap6-TI-83.pdf (textual description).
The answer is $129,290 (rounded).
(b) The normal distribution is a bell-shaped curve.
In this question, you are given the area under the specified normal distribution curve
on the left of the row z-score of 0.10.
It means that they want you find the value of the inverse accumulated normal distribution function
at the mean of 80,000, standard deviation of 24,000, and the row z-score of 0.10.
It will show you the entire process in visual form,
so you will see and understand what you are doing and you will be able to learn.
+---------------------------------------------------------------------+
| Using this online calculator is indispensable as a teaching tool |
| for a beginner student to learn the subject. |
+---------------------------------------------------------------------+
Alternatively, if you just have some introductory conceptual knowledge, you can use your standard calculator.
The function to use is invNorm(mean,SD,z).
If you need instructions on how to use it, you can find them in the internet at this link
https://www.youtube.com/watch?v=RPzxs-Hd8s0 (video-lesson for Casio calculators) or
https://www.youtube.com/watch?v=7mkfGJO8ehM (video-lesson for TI-83 or TI-84) or
https://cosmosweb.champlain.edu/people/stevens/WebTech/TIFiles/Chap6-TI-83.pdf (textual description).
The answer is $49,243 (rounded).
Solved.
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Let me explain my teaching conception about this subject.
I assume that there are two major different reasons why visitors come to this forum
with such problems/questions.
One reason is when they want simply get the number/(the answer) without any learning.
It is a sad case, but it is still a real life. Such visitors do not need any teaching/explanations, at all.
The other reason is when the visitors still want to learn.
As a rule, such beginner visitors don't know what the problem really wants from them;
don't know how to approach, don't know what to do, and don't know how to do.
For such beginner visitors, I strongly recommend to start with the online solver/calculator.
It provides a visual support, which works better than any teacher.
In addition, this visual support prevents you from making errors.
After inputting, it shows the area of interest as a shaded area, so you can see what you do.
After playing with this solver/calculator 3-5-10 times, you will understand the subject enough
to make your further calculations using your standard calculator.
After that, you may use your standard calculator as your basic tool, and you can practice
with it to prepare yourself for exam.
After that, you may use the online calculator for the checking purposes, only.
It is a solid way for beginners to become a professional master in the field and then teach others.
Answer by ewatrrr(24785)  (Show Source):
You can put this solution on YOUR website! Normal Distribution: µ = 80,000 and σ =24,000
A Percentage is the area under the Standard Normal Curve
to the left of the z-score.
For example z = 2.0537 (when 2% is to the right & 98% is to the left)
Calculator function: Invnorm(.98) = z = 2.0537 rounded
amount = 2.0537*(24000) + 80,000 = $129,289 (nearest dollar)
Using TI or similarly an inexpensive calculator like an Casio fx-115 ES plus
is the key to Your Success working with the various Distributions.
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