Given that the mean of the normal variate X is 10 and the standard deviation is 2, then what will be the z-score of the data point 16?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3
The z-score (standard normal variate) is
\( \displaystyle z=\frac{X-\mu}{\sigma} \)
\( \displaystyle =\frac{16-10}{2}=3 \)
Why the other options are incorrect
Option (1) -3 — Incorrect. −3 comes from \( \frac{\mu-X}{\sigma} \), the subtraction in the wrong order; 16 is above the mean, so its z-score is positive.
Option (3) 1.4 — Incorrect. The z-score is 3, not 1.4.
Option (4) 0.5 — Incorrect. The z-score is 3, not 0.5.