Bell Curve - Normal Distribution

Y = Ke^{-(X-M)²/(2σ²)}

X,Y	are the curve's x,y coordinates (used for plotting, etc.)
K	is the maximum Y coordinate; used to scale the Y coordinates (height in Y units)
M	is the curve's mathematical mean (X coordinate of the mean)
σ	is the curve's standard deviation; determines how fat or skinny the curve is (width in X units)
e	is Euler's number; is a constant; is an irrational number (defined in the Python numpy module and other libraries)

From: math.stackexchange.com

With this equation the user can:

select what part of the curve to calculate; (used for plotting, etc.)
set X coordinate for the curve's mean
set maximum size of the curve's Y coordinates
set how fat of skinny the curve is; standard deviation (in X units)

Python3

# -------------------------------------------------------------------
# ---- return the bell curve's y coordinate for a given x coordinate
# ---- x     bell curve x coordinate
# ---- ymax  bell curve data arithmetic mean (y coordinate)
# ---- mean  bell curve data arithmetic mean (x coordinate)
# ---- sd    bell curve data standard deviation
# -------------------------------------------------------------------

import numpy as np

def BellCurveValue(x,ymax,mean,sd):

    y = ymax * pow(np.e,-pow(x-mean,2.0)/(2.0*sd*sd))

    return y

# ------------------------------------------------------------------
# ---- return a list of random samples from a population list
# ----   poplst - population data list
# ----   samsiz - size of sample
# ------------------------------------------------------------------

import numpy as np
import random

def RandomSample(poplst,samsiz):

    poplen = len(poplst)

    # ---- collect samsiz samples

    sam = []                   # list of samples

    for _ in range(samsiz):

        i = random.randint(0,poplen-1)

        sam.append(poplst[i])

    # ---- calculate mean and standard deviation

    avg = np.mean(sam)     # average (mean)
    std = np.std(sam)      # standard deviation

    return (sam,avg,std)

Useful Links

Formula for the Normal Distribution or Bell Curve
Note: This has a slightly different version of the equation. Read the article for more information.

Standard Deviation (Wikipedia)

Normal Distribution (Wikipedia)