Question

GRE vs GMAT ~ Tony and Taylor are arguing about who among them is better at quantitative reasoning. Tony scores 615 on the quantitative reasoning part of the GRE test. The GRE quantitative reasoning scores have a mean of 600 and a standard deviation of 120. Taylor takes the GMAT quantitative reasoning test and scores 294. GMAT quantitative reasoning scores have a mean of 225 and a standard deviation of 61. Calculate the z-score for Tony's GRE quantitative reasoning score. Give your answer to 4 decimal places.

Answer 1

The z-score for Tony's GRE quantitative reasoning score is 0.1250, which indicates that Tony scored above the mean on the GRE quantitative reasoning test.

Step-by-step explanation:

To calculate the z-score for Tony's GRE quantitative reasoning score, we use the formula z = (X - μ) / σ, where X is Tony's score, μ (mu) is the mean score, and σ (sigma) is the standard deviation.

Tony's GRE score, X, is 615. The mean GRE score, μ, is 600, and the standard deviation, σ, is 120.

So, the z-score for Tony's score is:

z = (615 - 600) / 120

z = 15 / 120

z = 0.125

Therefore, to four decimal places, Tony's z-score is 0.1250.

The z-score tells us how many standard deviations Tony's score is from the mean. Since the z-score is positive, we know that Tony scored above the mean for the GRE quantitative reasoning test.

Answer 2

`Z = 0.125`

Step-by-step explanation:

Z - score

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.

Calculate the z-score for Tony's GRE quantitative reasoning score.

This is Z when
`X = 615, \mu = 600, \sigma = 120`

So

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

`Z = (615 - 600)/(120)`

`Z = 0.125`