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?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the mean is 522.7 kg
the variance is 100 square kg.
the standard deviation is the square root of the variance = 100 kg
raw score you want to test against is 521 kg
z-score formula is z = (x - m) / s
x is the raw score
m is the mean
s is the standard deviation.
formula becomes z = (521 - 522.7) / 100 = -.017
area to the left of a z-score of -.017 = .493218 rounded to 6 decimal places.
that's the probability that the weight of concrete poured into a mold is less than 521 kg.
that's equal to 49.32% rounded to 2 decimal places.
Answer by ikleyn(52890)  (Show Source):
You can put this solution on YOUR website! .
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  = 10 kilograms.
So, I came to bring a correct solution.
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 ANSWER 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.
At this point, the solution is completed.
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From my post, you learned two methods/approaches of solving such problems.
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