How to get the probability from the mean of a random variable?

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SUMMARY

The discussion centers on calculating the upper bound probability that a student's test score exceeds 75, given a mean score of 65. Participants highlight the absence of specific equations or standard deviation data, which complicates the analysis. The consensus leans towards utilizing Chebyshev's inequality to derive the upper bound probability, despite the lack of variance information. The conversation emphasizes the importance of understanding distribution characteristics, particularly in relation to normal distribution assumptions.

PREREQUISITES
  • Understanding of random variables and their properties
  • Familiarity with Chebyshev's inequality
  • Basic knowledge of probability theory
  • Concept of mean and its implications in statistical analysis
NEXT STEPS
  • Study Chebyshev's inequality and its applications in probability
  • Learn about calculating variance and standard deviation for random variables
  • Explore the characteristics of normal distribution and its significance in statistics
  • Investigate methods for estimating probabilities from mean values
USEFUL FOR

Students studying statistics, educators teaching probability concepts, and anyone interested in understanding the implications of mean values in random variable analysis.

EGD Eric
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Homework Statement


From past experience, a professor knows that the test score of students taking a final examination is a random variable with mean 65.

Give an upper bound on the probability that a student's test score will exceed 75.


Homework Equations



None that I know of.

The Attempt at a Solution


I tried seeing if I could get the standard deviation, in the hopes that I could do something with that, but I don't know how to even get the variance.

I've tried looking at this problem from a bunch of different angles, writing it out, etc.. I'm seriously stuck! Any help or hints would be greatly appreciated!
 
Physics news on Phys.org
Is this normally distributed?
 
I think so.
 

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