Question 1199260
.
In a factory, the weight of the concrete poured into a mold by a machine 
follows a normal distribution with a mean of 522.7 kg and a variance of 100 kg squared. 
What is the probability that the weight of concrete poured into a mold is less than 521 kg?
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        The solution by @Theo is incorrect,  since  Theo mistakenly uses the value of 100 

        as the standard deviation in his calculations,  while the correct value

        for the standard deviation in this problem is    {{{sqrt(100)}}} = 10 kilograms.


        So,  I came to bring a correct solution.



<pre>
Every normal distribution curve is a bell shaped curve.

In this problem, they want you determine the area under this specific normal curve
below the raw mark of 521 kg.  This area is the sought probability.


Go to web-site https://onlinestatbook.com/2/calculators/normal_dist.html
and find there free of charge online calculator, specially developed for this purpose.

Input the mean value 522.7 and the standard deviation value of 10;
input 521 in the window "Below"; then click "Recalculate".

You will get the <U>ANSWER</U>  0.4325  in the window "Probability".

The auxiliary plot will show you the area of the interest.


Now, when you know "what to do", I will tell you that you can get the same result 
using your calculator  TI-83 or TI-84 (or whatever).

For it, use the calculator' standard function normalcdf with parameters

                      z1    z2   mean   SD   

     P = normalcdf( -9999,  521, 522.7, 10) = 0.4325.

You will get the same value of the probability 0.4325 from your calculator.
</pre>

At this point, the solution is completed.



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From my post, you learned two methods/approaches of solving such problems.