# Percentile Rank

In a normal distribution with mean 30 and variance 25, at what percentile rank does a score of 42 fall?

Among twenty-five articles, nine are defective, six having only minor defects and three having major defects. Determine the probability that an article selected at random has major defects given that it has defects.

In a normal distribution with mean 3 and variance 49, what are the upper and lower limit scores for the middle 50% of the data?

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#### Solution Preview

In a normal distribution with mean 30 and variance 25, at what percentile rank does a score of 42 fall?

Solution:

Let X be the random variable. Then X~N(30, 25). We can compute that the probability of X greater than 42 is

Pr(X>42)=Pr((X-30)/5>12/5)

=0.0082

So, Pr(X<42)=1-Pr(X>42)=0.9918

Note: if X~N(30,25), then (X-30)/5~N(0,1), the standard normal ...

#### Solution Summary

This solution assists in determining probability and the upper and lower limit scores.