What is the Area Under the Curve for 1.5 Standard Deviations from Z=1?

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SUMMARY

The area under the standard normal curve within 1.5 standard deviations from z=1 is definitively 0.6853, corresponding to option D. To calculate this area, one must utilize statistical tables that provide values for the standard normal distribution, commonly referred to as Z-tables. The Gaussian function, represented by f(x) = (1 / (σ√(2π))) e^(-x²/(2σ²)), is essential for understanding the shape of the standard normal curve.

PREREQUISITES
  • Understanding of standard normal distribution
  • Familiarity with Z-tables
  • Knowledge of the Gaussian function
  • Basic statistics concepts, including standard deviations
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  • Research how to use Z-tables for calculating areas under the curve
  • Learn about the Gaussian Integral and its applications
  • Study the properties of the standard normal distribution
  • Explore the error function and its significance in statistics
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Students studying statistics, educators teaching statistical concepts, and anyone needing to understand the standard normal distribution and its applications in data analysis.

bluebear
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Hello,
I'm having trouble with this one question on my review sheet (yikes, and I have a chapter test on Statistics tomorrow!). The question is: What is the area under the standard normal curve that is within 1.5 standard deviations of z=1?

a) 0.2838 b) 0.3050 c) 0.5637 d) 0.6853 e) 0.7714

The answer is D, but I don't know how to get that answer. Anyway, if anyone can help, that'll be GREAT! Thanks so much!
 
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You can't really calculate this with paper and pen. However, there are tables that give you the area between different intervals. I'm not sure what the tables are referred to as, but you could try Googling. Also see Gaussian Integral and error function.

Note : the shape of the std. normal curve is the gaussian function :

f(x)= {\frac {1} {\sigma \sqrt{2\pi}} e^{-x^2/{2{\sigma}^2}}
 
Last edited:
Thanks!

Thanks for helping! I've finally figured out the answer! =) :smile: :surprise: :biggrin:
 

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