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
asked 2020-12-09
For a population with a mean of \(\displaystyle\mu={100}\) and a standard deviation of \(\displaystyle\sigma={20}\),
Find the X values.
\(\displaystyle{z}=-{.40}\).

Answers (1)

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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