Final exam scores in a mathematics course are normally distributed with a mean o

Question

Final exam scores in a mathematics course are normally distributed with a mean of 80 and a standard deviation of 13. Based on the above information and a Z-table, fill in the blanks in the table below.

Precision and other notes: (1) Percentiles should be recorded in percentage form to three decimal places.
(2) Note that this problem does not use the rough values of the 68-95-99.7 rule (that is, the empirical rule); instead you must use more precise Z-table values for percentiles.

Exam score Z-score Percentile 67 41 -0.67 2.28

Explanation / Answer

Consider the table:

If the x value is given, use z = (x - u)/sigma to get the z value, then use table/technology to get the percentile rank.

You can use x = u + z*sigma if z is given instead.

Exam Score Z score Percentile 67 -1 15.86553 41 -3 0.13499 71.29 -0.67 25.14289 54.012 -1.99908 2.28

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