Nomal curve (bell shaped curve) normal distribution statistics function?

TwPf

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I do not know the function of the normal distribution curve used to calculate z- scores and their corresponding area under the curve as percentiles.. Is it something like f(x) = ln(x) or something --> i know thats not it just providing a template for the answer i have been searching for. From there i need to find the definite integral from - infinite; to -2, for x, i know this should be .05 i just need the function to perform the equation/proof for an upcoming test, and i know how to find the definite integral i just had a question about the function
 
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