Answer :
A normal distribution is symmetric about its mean. This means that the mean is also the median of the distribution. By definition, half of the values lie below the median and half lie above it. Mathematically, if [tex]$X$[/tex] is a normally distributed random variable with mean [tex]$\mu$[/tex], then the cumulative distribution function (CDF) evaluated at [tex]$\mu$[/tex] is:
[tex]$$
P(X \leq \mu) = 0.5
$$[/tex]
This probability of [tex]$0.5$[/tex] corresponds to [tex]$50\%$[/tex].
Thus, [tex]$50\%$[/tex] of the values lie below the mean in a normal distribution.
[tex]$$
P(X \leq \mu) = 0.5
$$[/tex]
This probability of [tex]$0.5$[/tex] corresponds to [tex]$50\%$[/tex].
Thus, [tex]$50\%$[/tex] of the values lie below the mean in a normal distribution.
