For a population with a mean of \mu= 100 and a standard deviation of \sigma=20, Find the X values. z = -.40.

Question
Random variables
For a population with a mean of $$\displaystyle\mu={100}$$ and a standard deviation of $$\displaystyle\sigma={20}$$,
Find the X values.
$$\displaystyle{z}=-{.40}$$.

2020-12-10
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.

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