# Solving Normal Distribution Probability

The mean length of 600 stainless steel sticks is 181mm and the standard deviation is 60mm.Assuming that the length is normally distributed,

1) find the probability that a randomly chosen stick is between 150 and 190mm in length.

2)Given that the length of a particular stick is more than 195mm, find the conditional probability that is actual length exceeds 210mm.

I already solve part (1). For part 2 i dont know. Could someone help me out

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– You Sep 19 '12 at 16:58
not sure. It says conditional probability – David Sep 19 '12 at 16:59

Let $A$ be the event "greater than $195$" and let $B$ be the event "greater than $210$." We want $\Pr(B|A)$. By a standard formula, $$\Pr(B|A)=\frac{\Pr(A\cap B)}{\Pr(A)}.$$
Note that $\Pr(B\cap A)$ is just $\Pr(B)$. If you solved the first problem then you know how to find $\Pr(A)$ and $\Pr(B)$.
Remark: Intuitively, $\Pr(A)$ is the area under a certain "tail" of the normal. Our answer $\dfrac{\Pr(B)}{\Pr(A)}$ is just the ratio of the area past $210$ to the area past $195$.
So this is my steps : P(X>210|X>195)= P(Z>0.483|Z>0.233)=$$\frac{P(Z>0.483)}{P(Z>0.233)}$$.And i got the answer 0.7712. Is my answer right?? – David Sep 19 '12 at 17:26
$\Pr(A)$ is the probability of being more than $14$ above the mean, so it is $\Pr(Z\gt 14/60$. Now use normal tables or software. – André Nicolas Sep 19 '12 at 17:27