Obtain the value of the random variable X if the Z-score equals –0.40.

The value of the random variable X if the Z-score equals –0.40 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,

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

\(\displaystyle-{0.40}={\frac{{{X}-{100}}}{{{20}}}}\)

\(\displaystyle{X}-{100}=-{0.40}\times{20}=-{8}\)

\(\displaystyle{X}={100}-{8}={92}\)

The value of the random variable X if the Z-score equals –0.40 is 92.

The value of the random variable X if the Z-score equals –0.40 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,

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

\(\displaystyle-{0.40}={\frac{{{X}-{100}}}{{{20}}}}\)

\(\displaystyle{X}-{100}=-{0.40}\times{20}=-{8}\)

\(\displaystyle{X}={100}-{8}={92}\)

The value of the random variable X if the Z-score equals –0.40 is 92.