Answer to Question #201491 in Statistics and Probability for Cristine Mariel

Question

The results of the final exam in General Mathematics of the 12 sections of Grade 1

are normally distributed with u = 82and o = 13. What is the percentile rank of a score o

85

A percentile rank of 85 means you have to find the percentage of scores below 85. T

find the required area in the Z-table, transform 85 to a z-score

1. Convert the raw score of 85 to a z-score

2. Draw the normal curve showing the z-score.

3.Draw a line through the z-score and shade the required region.

(Note : In the problem, the required region is below the computed z-score since you are looking for the percentile rank)

4. Use the table and find the area that corresponds to the computed z-score.

5. Examine the shaded region and make an appropriate operation apply

6. Compute the percentile rank of the score. (Hint: Multiply the probability in decimal by 100 to get the desired percentage)

Answer 1

Let $X=$ score: $X\sim N(\mu, \sigma^2).$ Then $Z=\dfrac{X-\mu}{\sigma}\sim N(0, 1)$

Given $\mu=82, \sigma=13$

1.

$$z=\dfrac{x-\mu}{\sigma}=\dfrac{85-82}{13}\approx0.230769$$

2-3.

4-5.

$$P(X<85)\approx P(Z<0.230769)\approx0.591253$$

6.

$$0.591253\cdot100\%=59.1253\%$$