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?

Libby Owens
2022-07-22
Answered

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yermarvg

Answered 2022-07-23
Author has **19** answers

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: $X\sim N(75,{20}^{2})$.

The z-score = 1.5

The percentile rank corresponding to the z-score of 1.5 can be computed as:

${p}_{r}=100\times P(z<1.5)\phantom{\rule{0ex}{0ex}}=100\times 93319\phantom{\rule{0ex}{0ex}}=93.319\phantom{\rule{0ex}{0ex}}\approx 93.32$

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.

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: $X\sim N(75,{20}^{2})$.

The z-score = 1.5

The percentile rank corresponding to the z-score of 1.5 can be computed as:

${p}_{r}=100\times P(z<1.5)\phantom{\rule{0ex}{0ex}}=100\times 93319\phantom{\rule{0ex}{0ex}}=93.319\phantom{\rule{0ex}{0ex}}\approx 93.32$

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.

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