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.

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.