Slide the mean to move a bell curve and the standard deviation to change its width. The shaded area between two limits is the probability of landing there.
Normal (Gaussian) Distribution
Mean (μ):0.0
Std Dev (σ):1.0
Limit a:-1.0
Limit b:1.0
Properties & Integration
Parameters: μ = 0.0, σ = 1.0
Interval: [-1.0, 1.0]
F(1.0) = 0.8413
F(-1.0) = 0.1587
P(-1.0 ≤ X ≤ 1.0) = F(b) - F(a)
= 0.6827 (68.3%)
The Normal distribution is symmetric about its mean μ.
Try setting the interval to μ ± σ (e.g. μ=0, σ=1, a=−1, b=1) to verify the empirical rule: approximately 68% of the area lies within 1 standard deviation.
The Normal Distribution is defined by its center μ and spread σ. The probability corresponds to the shaded area under the curve. Note that the tails extend to negative and positive infinity, though they decay extremely fast.
