True or False: There is only one normal distribution.

Question

Question 9 options: False or True

Answer 1

If by normal distribution you mean a function of the form

 

f(x,μ,σ) = 1/[σ√(2π)]  exp[-(x - μ)² / (2σ²)]

 

where

 

μ = mean

σ =  standard deviation,

 

then it is TRUE that there is only one normal distribution, and the above equation is it.  However, there are many other distributions that have a general Gaussian shape, as in

 

g(x) = A exp[-a(x - x₀)²],

 

but those are not normal.  If I recall correctly, the area under the normal curve, from -∞ to +∞, must equal 1.  In general, the area under a Gaussian is not 1.

Answer 2

True, any other distribution is abnormal (isn't that a truism?)