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
asked 2021-02-05
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?

Answers (1)

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.
0

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