Question

Sam knows that the University he is applying to has a strict SAT cutoff. Note that the SAT is a standardized test that produces a normal distribution of scores. The University only accepts students who score in the top 10% of all SAT takers. Sam has his z-score from taking the SAT, he just wants to know if he's in the top 10%. How could Sam use the Unit Normal Table to answer his question?

Answer #1

The standard normal distribution table has the z scores and their corresponding percentiles.

The z score corresponding to 90th percentile is obtained by taking the value of z corresponding to the probability value 0.9000 (or the value closest to 0.9000) in the table. From the table, we get the z score corresponding to 90th percentile as 1.28.

This means, if an z score is less than or equal to 1.28, he/she is in the bottom 90% and if the z score is above 1.28, he/she is in top 10%.

Sam can use this information to see if he is in top 10%. If his z score is greater than 1.28, he is in top 10%

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