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Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 569 and standard deviation 106. Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 24.5 and standard deviation 2.4.

Required:
a. What is Elanor's standardized score?
b. What is Gerald's standardized score?

Respuesta :

Answer:

a). 1.05 Elanor's standardized score

b). 1.04 Gerald's standardized score

Step-by-step explanation:

According to the Question,

  • (a). Given that, Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with a mean of 569 and a standard deviation 106.

Thus, Elanor's standardized score is

[tex]Z=\frac{x-mean}{standard deviation}[/tex]

Z = (680-569) ÷ 106 ⇒ 111/106 ⇒ 1.047≈1.05

  • (b). Also Given that, Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with a mean of 24.5 and a standard deviation 2.4.

Thus, Gerald's standardized score is

[tex]Z=\frac{x-mean}{standard deviation}[/tex]

Z = (27-24.5) ÷ 2.4 ⇒ 2.5/2.4 ⇒ 1.041≈1.04

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