Question

For a population with a mean of \mu= 100 and a standard deviation of \sigma=20, Find the X values. z = -.50.

Random variables
ANSWERED
asked 2021-01-31
For a population with a mean of \(\displaystyle\mu={100}\) and a standard deviation of \(\displaystyle\sigma={20}\),
Find the X values.
\(\displaystyle{z}=-{.50}\).

Answers (1)

2021-02-01
Obtain the value of the random variable X if the Z-score equals –0.50.
The value of the random variable X if the Z-score equals –0.50 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,
\(\displaystyle{z}={\frac{{{X}-\mu}}{{\sigma}}}\)
\(\displaystyle-{0.50}={\frac{{{X}-{100}}}{{{20}}}}\)
\(\displaystyle{X}-{100}=-{0.50}\times{20}=-{10}\)
\(\displaystyle{X}={100}-{10}={90}\)
The value of the random variable X if the Z-score equals –0.50 is 90.
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