Answer:
As we can see the z score for Ferdinad is higher than the z score for Emilia so on this case we can conclude that Ferdinand was better compared with his group of reference.
Step-by-step explanation:
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".
Solution to the problem
Emilia case
Let X the random variable that represent the scores of a test, and we know that
Where and
The z score formula is given by:
Since Emilia made 83 points we can find the z score like this:
Ferdinand case
Let X the random variable that represent the scores of a test, and we know that
Where and
The z score formula is given by:
Since Ferdinand made 79 points we can find the z score like this:
As we can see the z score for Ferdinad is higher than the z score for Emilia so on this case we can conclude that Ferdinand was better compared with his group of reference.