The average score on your Math Exams was 75 with a standard deviation of 20. Assuming the scores are normally distributed. If your corresponding z-score was 1.5, and your corresponding raw score is 105, what is the percentile rank?

The average score on your Math Exams was 75 with a standard deviation of 20. Assuming the scores are normally distributed. If your corresponding z-score was 1.5, and your corresponding raw score is 105, what is the percentile rank?
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yermarvg
Average score, $\mu =75$
Standard deviation of scores, $\sigma =20$
Let X be the random variable that records scores obtained in exams.
The scores are normally distributed. Therefore, the distribution of X is: $X\sim N\left(75,{20}^{2}\right)$.
The z-score = 1.5
The percentile rank corresponding to the z-score of 1.5 can be computed as:
${p}_{r}=100×P\left(z<1.5\right)\phantom{\rule{0ex}{0ex}}=100×93319\phantom{\rule{0ex}{0ex}}=93.319\phantom{\rule{0ex}{0ex}}\approx 93.32$
Thus, the percentile rank corresponding to z = 1.5 is 93.32.
The computed rank depicts that that around 93.32% of the data have z-score less than 1.5 or have marks less than 105.