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Chapter 6: Q.6.4 (page 370)

In 2012, 1,664,479 students took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean 碌=496 and a standard deviation 蟽=114. Let X = a SAT exam verbal section score in 2012. Then X~N(496,114). Find the z-scores for x1=325 andx2=366.21. Interpret each z-score. What can you say about x1=325 and x2=366.21 as they compare to their respective means and standard deviations ?

Short Answer

Expert verified

Student 2 is closer to mean hence student 2 had better score.

Step by step solution

01

Given Information 

The distribution of scores in the verbal section of the SAT had a mean 碌=496 and a standard deviation 蟽=114.

02

Explanation

It is given that,

X~N(496,114)

Where,

渭=496

蟽=114

And,

x1=325

So, the z-score at x1=325will be:

z-score=325-渭蟽

=325-496114

=-171114

鈮�-1.5

03

Explanation

x2=366,21

So, the z-score at x2=366.21will be:

z-score=366.21-渭蟽

=366.21-496114

鈮�-1.14

Therefore, the value of the z-score at x2=366.21is -1.14.

On comparing the both z-score it is clear that student 2with x2=366.21is closer to mean than the student 1and since student 2is closer to mean hence student 2had better score.

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