Question

For a population with a mean of \(\displaystyle\mu={100}\) and a standard deviation of \(\displaystyle\sigma={20}\),
Find the X values.
\(\displaystyle{z}=+{1.80}\).

Answer 1

Obtain the value of the random variable X if the Z-score equals 1.80.
The value of the random variable X if the Z-score equals 1.80 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,
\(\displaystyle{z}={\frac{{{X}-\mu}}{{\sigma}}}\)
\(\displaystyle{1.80}={\frac{{{X}-{100}}}{{{20}}}}\)
\(\displaystyle{X}-{100}={1.80}\times{20}={36}\)
\(\displaystyle{X}={100}+{36}={136}\)
The value of the random variable X if the Z-score equals 1.80 is 136.