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Chapter 2: Q. 9 (page 139)

Questions T2.9 and T2.10 refer to the following setting. Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990swas 470and the standard deviation was 110. In 2009, the mean was 515 and the standard deviation was 116 .
T2.9. What is the standardized score ( z-score) for a student who scored 500 on the old SAT scale?
(a) -30
(b) -0.27
(c) -0.13
(d) 0.13
(e) 0.27

Short Answer

Expert verified

The standardized score is 0.27. So, the option (e) is correct.

Step by step solution

01

Given information

SAT scores were based on a scale established many years ago before the scale was altered in 1995. In 1990, the mean math score on the previous scale was 470, with a standard deviation of 110. The mean in 2009 was 515, with a standard deviation of 116.

02

Explanation

From the oldSATs:
渭=Mean=470

蟽=Stanadarddeviation=110

x=500

The standardized score is the score multiplied by the standard deviation and divided by the mean:

z=x-渭蟽=500-470110=30110=311鈮�0.27

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