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Calculation of Percentile Rank

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Misery loves company. It is time for the PE (professional engineer's exam). The results of the national test were normally distributed around the mean score of 70. A score of 60 points was a passing score. Since I know someone the knows someone, I found out that my score was 80 and I rated in the 80 percentile (bottom of the top 20%). My roommate (Joey) was worried, so we went to check the results board. The results were listed by candidate percentiles and did not list the actual scores. Joey was listed in the 30 percentile (top of the lower 30% bracket). Joey looked confused and demoralized. Did he pass the exam?

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The solution gives the details of calculation of percentile score and Z score.

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