# 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?

Question
Random variables
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?

2021-02-06
Step 1
Solution:
It is given that,
Population mean, $$\displaystyle\mu={278}$$
Standard deviation, $$\displaystyle\sigma={25}$$
Step 2
Now, the Z value for a random variable to be $$\displaystyle{X}={185}$$ can be calculated as:
$$\displaystyle{Z}={\frac{{{X}-\mu}}{{\sigma}}}$$
$$\displaystyle={\frac{{{185}-{278}}}{{{25}}}}=-{3.72}$$
Hence, the Z value for a random variable to be 185 is -3.72.

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