Question

In: Statistics and Probability

The Academy of Mathematics is looking to select an individual for an award based on their...

The Academy of Mathematics is looking to select an individual for an award based on their performance on their Grade 12 Data test. Pictured are the test results. How can the Academy decide which candidate is better suited for the award? Justify mathematically.

Nathan, from Kitchener scored 85% on his test that had a mean score of 71% and a standard deviation of 4%.

Nolan, from Elmira scored 87% on his test that had a mean score of 71% and a standard deviation of 7%.

Expert Solution

The Academy Of Mathematics is looking to select an individual for an award based on their performance on their Grade 12 Data Test.

It is given that,

Nathan, from Kitchener scored 85% on his test that had a mean score of 71% and a standard deviation of 4%.

Nolan, from Elmira scored 87% on his test that had a mean score of 71% and a standard deviation of 7%.

Now, we have to decide who is better suited for the award.

Here, we have to compare two scores who have different means and standard deviations.

Now, the formula of z-score is given by

Where, x is the observed score; m is the mean; and s is the standard deviation.

The z-score for Nathan is

The z-score for Nolan is

We note that the z-score for Nathan is greater than the z-score for Nolan.

The answer is

Nathan is best suited for the award.

orchestra answered 1 year ago

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