Question

In Exercise 3.3 we saw two distributions for GRE scores: N(μ=151,σ=7) for the verbal section of the exam and N(μ=153,σ=7.67) for the quantitative section. Use this information to compute each of the following. Round all your answers to 2 decimal places.

a) The score of a student who scored in the 90 -th percentile on the Quantitative Reasoning section.

Answer 1

To find the score of a student who scored in the 90th percentile on the Quantitative Reasoning section, calculate the z-score associated with the percentile and use that to find the corresponding score value.

Step-by-step explanation:

To find the score of a student who scored in the 90th percentile on the Quantitative Reasoning section, we need to find the z-score associated with the percentile and then use that z-score to find the corresponding score value.

First, we calculate the z-score using the formula: z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation. For the Quantitative Reasoning section, we have μ = 153 and σ = 7.67.

Next, we find the z-score associated with the 90th percentile using a z-score table or calculator. Let's say the z-score is z90. Finally, we use the formula: x = z90 * σ + μ to find the score corresponding to the z-score. Round the answer to 2 decimal places.