Rachael got a 550 on the analytical portion of the graduate record exam (gre). if gre scores are normally distributed and have mean μ = 600 and standard deviation σ = 25, what is her standardized score?

Z=-2

This value means that the score of Rachel 550 it's 2 deviations below the mean of the population

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

represent the population mean for the Graduate Record Exam (GRE)

represent the population standard deviation for Graduate Record Exam (GRE)

2) Solution to the problem

Let X the random variable that represent the Graduate Record Exam (GRE) of a population, and for this case we know the distribution for X is given by:

Where and

We want to find the z score for a score of 550. And in order to do this we need to apply the formula for the z score given by:

If we apply this formula to our probability we got this:

So the answer for our case would be Z=-2

This value means that the score of Rachel 550 it's 2 deviations below the mean of the population

5+2x=a

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