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The correct answer is one of the following. Which one?
The average score on the ACT test is 21 with a standard deviation of 2 points.
What score must you get to be in the top 10% of scores (rounded to the nearest whole number)?
A) 19
B) 23
C) 18
D) 24
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The normal distribution is a bell-shaped curve.
In this question, you are given the area of 0.1 under the specified
normal distribution curve on the right of the unknown row z-score.
They want you find the value of the inverse accumulated normal distribution function
at the mean value of 21, standard deviation of 2, and the given area of 1-0.1 = 0.9.
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. |
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Alternatively, if you just have some introductory conceptual knowledge, you can use
your standard calculator. The function to use is invNorm(mean=21,SD=2,Area=0.9).
The answer is z-score = 23.5631. It means that the rounded score is 24 (option (D)). ANSWER
Solved, with explanations.
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By the way, instruction on rounding, given at the end of your post is INCORRECT.
It says " round to the nearest whole number ".
The correct rounding in this problem is " round to the nearest greater integer number ".
Fortunately, in this concrete problem both rounding lead to the same result;
but to be consistent with the context, the instruction in the post must be repaired.