# Thread: standardizing normal distribution problem

1. ## standardizing normal distribution problem

Scores on test are normally distributed with a mean of 68 and a standard deviation of 8. Find the probability that a student scored at least 75 on the test given that the student scored at least 70.

Is the bound for this question p(70<X<75) ? Seems like it should be p(X>75), but I'm not sure of what to do with the extra given data.

2. Originally Posted by shawli
Scores on test are normally distributed with a mean of 68 and a standard deviation of 8. Find the probability that a student scored at least 75 on the test given that the student scored at least 70.

Is the bound for this question p(70<X<75) ? Seems like it should be p(X>75), but I'm not sure of what to do with the extra given data.
Apply Bayes Theorem:

$\Pr(X > 75 | X > 70) = \frac{\Pr(X > 75 \text{ and } X > 70)}{\Pr(X > 70)} = \frac{\Pr(X > 75)}{\Pr(X > 70)}$.