Question 1204309
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Answer: <font color=red size=4>0.3907</font>



Explanation


There are a few methods we could use.


Method 1 is to use a Z table such as this
<a href = "https://www.ztable.net/">https://www.ztable.net/</a>
to find that
P(Z < 0.00) = 0.5
P(Z < 1.23) = 0.89065


So,
P(a < Z < b) = P(Z < b) - P(Z < a)
P(0 < Z < 1.23) = P(Z < 1.23) - P(Z < 0)
P(0 < Z < 1.23) = 0.89065 - 0.5
P(0 < Z < 1.23) = 0.39065
P(0 < Z < 1.23) = <font color=red>0.3907</font>



Method 2 involves a calculator such as this one
<a href= "https://davidmlane.com/normal.html">https://davidmlane.com/normal.html</a>
The mean and standard deviation are 0 and 1 respectively.
Click the "between" and fill in the values 0 and 1.23 to have <font color=red>0.3907</font> show up.


Another calculator you can use is a TI83 or TI84.
Refer to this article.
<a href = "https://www.statology.org/normal-probabilities-ti-84-calculator/">https://www.statology.org/normal-probabilities-ti-84-calculator/</a>
Use the normalCDF function to get the area under the curve.
The input that you'll type in is:  <font color=red>normalCDF(0,1.23)</font>
Or optionally you could type in <font color=red>normalCDF(0,1.23,0,1)</font>
The TI84 should display the approximate result 0.3906513828 which rounds to <font color=red>0.3907</font>


Or you could use a spreadsheet.
The spreadsheet function you'll use is called <font color=red>normDist</font>
Refer to this page for more info
<a href="https://www.statology.org/normal-distribution-probability-excel/">https://www.statology.org/normal-distribution-probability-excel/</a>


Yet another method is WolframAlpha
Type in <font color=red>P(0 < z < 1.23)</font> and you should get roughly 0.390651 which rounds to the answer shown above.
Caution: WolframAlpha is a great resource, but it has a glaring flaw. The graph shown on the page is not correct. The normal distribution curve should be entirely above the x axis. I don't know why some parts of it are below the x axis. I would hope the people running that website would fix the error soon. Rely on the diagram produced by the davidmlane website.


*[illustration Screenshot_324.png]


*[illustration Screenshot_325.png]


As you can see, there are a lot of ways to calculate the normal distribution probabilities. 
Feel free to explore other options.
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