I don't quite understand how to do the following question. How I tried to do it is to imagine the normal distribution curve, with the highest peak at 4. I understand that |Q| means the absolute value of it, but I don't know how to do it in relation to the normal distribution curve.
If Q~N $(4,160)$, (a) find $P (5<|Q|) $, (b) hence find $P(Q>5 | 5<|Q|)$
I tried using the calculator and using normalcdf $(5, 1E99, 4, \sqrt160)$, but I got the wrong answer.
The correct answer for (a) 0.707 (b) 0.663
Please advise. Sorry in advance for any wrong tags or title. Trying to improve on it.
If $|Q|>5$, then you know either $Q>5$ or $Q<-5$. Thus find both of these probabilities separately using properties of the normal distribution, and sum them to get your answer for (a). For part (b), you will need to use the formula for conditional probabilities, namely $$ P(Q>5| 5<|Q|)=\frac{P(Q>5\text{ and }5<|Q|)}{P(5<|Q|)}. $$ Since $Q>5$ implies $5<|Q|$, this reduces to $$ P(Q>5| 5<|Q|)=\frac{P(Q>5)}{P(5<|Q|)}. $$