Question

in 2018 GRE scores were normally distributed with a mean of 303, and standard deviation of 13. Standford University Graduate school only cosiders students that score in the top 2.5% of all GRE test takers. What is the minimum score needed to be considered for admission to Stanfords graduate school?

Answer 1

The minimum score needed to be considered for admission to Stanfords graduate school is 328.48.

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 303, \sigma = 13`

What is the minimum score needed to be considered for admission to Stanfords graduate school?

Top 2.5%.

So X when Z has a pvalue of 1-0.025 = 0.975. So X when Z = 1.96

`Z = (X - \mu)/(\sigma)`

`1.96 = (X - 303)/(13)`

`X - 303 = 13*1.96`

`X = 328.48`

The minimum score needed to be considered for admission to Stanfords graduate school is 328.48.