The value of the random variable X if the Z-score equals –0.50 is obtained below as follows:

Let X denotes the random variable with the population mean of 100 and standard deviation of 20.

That is, \(\displaystyle\mu={100}\), \(\displaystyle\sigma={20}\).

The required value of X is,

\(\displaystyle{z}={\frac{{{X}-\mu}}{{\sigma}}}\)

\(\displaystyle-{0.50}={\frac{{{X}-{100}}}{{{20}}}}\)

\(\displaystyle{X}-{100}=-{0.50}\times{20}=-{10}\)

\(\displaystyle{X}={100}-{10}={90}\)

The value of the random variable X if the Z-score equals –0.50 is 90.