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

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The discussion revolves around calculating the area under the standard normal curve within 1.5 standard deviations of z=1. The correct answer is identified as 0.6853, but the original poster was unsure how to arrive at this conclusion. It is noted that calculating this area manually is impractical, and reference to statistical tables or online resources is suggested for assistance. The Gaussian function is mentioned as the mathematical basis for the standard normal curve. Ultimately, the poster successfully finds the answer with help from the community.
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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}}
 
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Thanks!

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

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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