Obtain the value of the random variable X if the Z-score equals 1.50.

The value of the random variable X if the Z-score equals 1.50 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,

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

\(\displaystyle{1.50}={\frac{{{X}-{100}}}{{{20}}}}\)

\(\displaystyle{X}-{100}={1.50}\times{20}={30}\)

\(\displaystyle{X}={100}+{30}={130}\)

The value of the random variable X if the Z-score equals 1.50 is 130.

The value of the random variable X if the Z-score equals 1.50 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,

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

\(\displaystyle{1.50}={\frac{{{X}-{100}}}{{{20}}}}\)

\(\displaystyle{X}-{100}={1.50}\times{20}={30}\)

\(\displaystyle{X}={100}+{30}={130}\)

The value of the random variable X if the Z-score equals 1.50 is 130.