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The rate of return for firms on the stock market is normally distributed
with a 5% average rate and standard deviation of 2%.
What rate of return would put a firm in the top 20%. Please show steps
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They want you determine a raw mark on x-axis such that the area
under this normal curve on the right from this raw mark be exactly 20%, or 0.05.
For it, you may use the standard function invNorm of your regular calculator TI-83/84.
The format of this function is raw mark = invNorm(area, mean, SD).
So, you write raw mark = invNorm(0.95, 0.05, 0.02).
Here first value "0.95" denotes the area under the normal curve on the left of the raw mark;
second value "0.05" denotes the 5% = 0.05 mean;
third value "0.02" denotes standard deviation of 2% = 0.02.
Doing this way, you get raw mark = 0.083 (rounded).
We write 0.95 for the first argument, because the function invNorm
takes/accepts as the first argument the area on the LEFT of the raw mark 0.95 = 1 - 0.05.
Thus, the rate of return must be at least 0.083, or 8.3% in order for the firm be in the top 20%.
Alternatively, instead of using your regular calculator TI-83/84, you may use online
(free of charge) calculator at this web-site
https://davidmlane.com/hyperstat/z_table.html
This online calculator has intuitively clear interface and shows the area of interest,
so you never will make mistake and will clearly understand what you are doing and why.
Use this online calculator in the "Value from area" mode.
This online calculator is a perfect teacher, so, if you are a beginner student in such calculations,
you will learn the subject QUICKLY.
Therefore, I advise you to start using this online calculator. Later, as you gain a necessary experience,
you may return to regular calculators TI-83/84.
Solved, with explanations.