# For a population with a mean of \mu= 100 and a standard deviation of \sigma=20, Find the X values. z = +.75.

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.
$$\displaystyle{z}=+{.75}$$.

2021-02-06
Obtain the value of the random variable X if the Z-score equals 0.75.
The value of the random variable X if the Z-score equals 0.75 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,
$$\displaystyle{z}={\frac{{{X}-\mu}}{{\sigma}}}$$
$$\displaystyle{0.75}={\frac{{{X}-{100}}}{{{20}}}}$$
$$\displaystyle{X}-{100}={0.75}\times{20}={15}$$
$$\displaystyle{X}={100}+{15}={115}$$
The value of the random variable X if the Z-score equals 0.75 is 115.

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