Question

The scores on a math test are normally distributed with a mean of 64 and a standard deviation of 8. Tara scored 52 on the test. Jamal scored 82 on the test. Samuel scored 66 on the test. Find the standard (z) score for each student and answer the questions.
a. What percent of students did Tara score better than?
b. What percent of students scored better than Jamal?
c. What percent of students did Samuel score better than?


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Answer 1

A z-score is the number of standard deviations from the mean a data point is.

Standard deviation explains by how much the members of a group differ from the mean value for the group.
Using the z-score formula:
                                           z = ( x  - μ ) ÷ σ
Where;
            x = score
            μ = Mean
            σ = Standard deviation 

Z- Score (Tara) = ( 52 - 64 ) ÷ 8
                         = - 12 ÷ 8
                         = - 1.5 

Z- Score (Jamal)  = ( 82 - 64 ) ÷ 8
                             = 18 ÷ 8
                             = 2.25 

Z- Score (Samuel) = ( 66 - 64 ) ÷ 8
                               = 2 ÷ 8
                               = 0.25