Question

The Graduate Record Examination (GRE) is a standardized test that students usually take before entering graduate school. An article reveals that the scores on the verbal portion of the GRE are (approximately) normally distributed with mean 462 points and standard deviation 119 points.

(i) Find the 3rd decile for these scores.

(ii) Find the probability that the scores are between 380 and 520 points.

Answer 1

This problem uses the concept Normal Distribution, first we calculate the z score , then we find the probability using the z scores

i) 3rd Decile means 30% of the values below it, here we need to find the score X , such that 0.30 is the probability that a score is below X

First observe the z table below, the z score correspoding to a probability value of 0.30 is -0.52

if we use TI84 Calculator we get -0.5244

ii)