Chapter 6.3, Problem 9GP

Solution

To provide: The reason of $P\left(z\le 0\right)=0.50$

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme.

The graph of the normal distribution is.

  

For the normal distribution, total area under the curve is 1. Also, the normal distribution is symmetric to the origin it means that 50% of its area lies at the right and 50% at the left. Thus, $P\left(z\le 0\right)=0.50$