This is an interesting question from ACJC’2014 Prelim Exam. I feel that it test a lot on students’ understanding of the normal distribution curve.

The height $X$ , in centimetres, of a randomly chosen girl in HTAM Junior College is normally distributed with mean $\mu$ cm and standard deviation $\sigma$cm.

Given that $latex P(X > \mu – \sigma) + P(x > \mu + \sigma) + P(\mu < X < \mu +2 \sigma)=1.38$, find the $latex P(X > \mu + 2\sigma)$. Hint: Draw the curve and shade it out according. 🙂