X is a normal variate with mean 45 and standard deviation 6. The value of the standard normal variate Z corresponding to \(X = 54\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1.5
The standard normal variate is
\( \displaystyle Z = \frac{X - \mu}{\sigma} \)
With \(\mu = 45\), \(\sigma = 6\) and \(X = 54\):
\( \displaystyle Z = \frac{54 - 45}{6} \)
\( \displaystyle = \frac{9}{6} = 1.5 \)
Z is positive because 54 lies above the mean.