# For normal distribution with a mean of 278 and a standard deviation of 25, what is the Z value for a random value to be 185?

For normal distribution with a mean of 278 and a standard deviation of 25, what is the Z value for a random value to be 185?
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Pohanginah
Step 1
Solution:
It is given that,
Population mean, $\mu =278$
Standard deviation, $\sigma =25$
Step 2
Now, the Z value for a random variable to be $X=185$ can be calculated as:
$Z=\frac{X-\mu }{\sigma }$
$=\frac{185-278}{25}=-3.72$
Hence, the Z value for a random variable to be 185 is -3.72.
Jeffrey Jordon