X is a normal variate with mean 60. If the standard normal variate corresponding to \(X = 48\) is \(Z = -1.5\), then the standard deviation of X is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 8
The standard normal variate is \(Z = \frac{X - \mu}{\sigma}\). With \(\mu = 60\), \(X = 48\) and \(Z = -1.5\):
\( \displaystyle -1.5 = \frac{48 - 60}{\sigma} \)
\( \displaystyle -1.5 = \frac{-12}{\sigma} \)
\( \displaystyle \sigma = \frac{12}{1.5} = 8 \)