Solving Probability Problems: Normal Distributions and the Chance of B < A

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SUMMARY

The discussion focuses on calculating the probability that a value drawn from normal distribution B (Norm(13; 0.9)) is less than a value drawn from normal distribution A (Norm(12; 0.4)). The solution involves determining the distribution of the difference between the two independent random variables, specifically calculating the probability P(z < 0), where z = x - y. The key takeaway is that z will also follow a normal distribution, allowing for the application of standard probability techniques to find the desired probability.

PREREQUISITES
  • Understanding of normal distributions, specifically Norm(12; 0.4) and Norm(13; 0.9)
  • Knowledge of independent random variables and their properties
  • Familiarity with calculating probabilities using normal distribution
  • Ability to work with the concept of the difference of two random variables
NEXT STEPS
  • Learn how to derive the distribution of the difference of two independent normal variables
  • Study the properties of normal distributions and their applications in probability
  • Explore the use of the cumulative distribution function (CDF) for normal distributions
  • Practice calculating probabilities using statistical software or tools like R or Python's SciPy library
USEFUL FOR

Students studying statistics, data analysts, and anyone interested in understanding probability calculations involving normal distributions.

Marije
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Probability question

I can't figure out how to solve this problem.

Given are two normal distributions, A: Norm(12; 0,4) and B: Norm(13; 0,9).
If we pick one from A and one from B what's the chance B < A?
I don't know how to do this because we haven't learned a formula or anything for the graphs. I think what they're asking for is to calculate the area I coloured in this picture:
http://img211.imageshack.us/img211/1692/kansberekeningsk5.jpg
Sorry for the crappy drawing skills. I hope you understand the idea anyway.
Is there any way to calculate it? ;x I'm lost.

Oops sorry I think I posted this in the wrong section... Sorry, I'm new here. I'm not sure if this should go here or in the homework section, since there are more questions like mine in this forum but it's homework so I don't know, sorry.
 
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Have you learned how to get the distribution for the sum (or difference) of two independent random variables, particularly of normal variables? If so, let x be chosen from A, y chosen from B, and let z=x-y. z will be normally distributed and you need to get prob (z<0).
 

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