How Do You Calculate Probability for a Normally Distributed Variable?

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SUMMARY

To calculate the probability for a normally distributed variable, specifically for the range P(10≤x≤12) with a mean (μ) of 11 and a standard deviation (σ) of 2, one must standardize the variable using the formula y = (x-μ)/σ. This transforms the variable into a standard normal distribution, where the relevant domain becomes -0.5 ≤ y ≤ 0.5. The final step involves consulting a standard normal distribution table to find the corresponding probability values.

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  • Understanding of normal distribution concepts
  • Familiarity with mean (μ) and standard deviation (σ)
  • Knowledge of standardization in statistics
  • Ability to read standard normal distribution tables
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  • Study the properties of normal distributions
  • Learn how to use z-scores for standardization
  • Practice calculating probabilities using standard normal distribution tables
  • Explore applications of normal distribution in real-world scenarios
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Students, statisticians, and anyone interested in understanding probability calculations for normally distributed variables.

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P(10≤x≤12)
σ=2,μ=11
x= a normally distrributed random variable

I don't even know where to begin to solve this. I was hoping someone could show me how and explain it to me like I am a 6 year old.
thanks everybody in advance.
 
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Let y = (x-μ)/σ. Then y is a standard normally distributed random variable. The domain of interest is then -1/2≤y≤1/2. Look up a table for the standard normal distribution to get the answer.
 

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