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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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    not sure. It says conditional probability2012-09-19

1 Answers 1

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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 $195$.

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    Ok Sir thank you very much for your help and effort. You really help me out well!!! Thanks again2012-09-19