contestada

Raul received a score of 77 on a history test for which the class mean was 70 with a standard deviation of 6. He received a score of 79 on a biology test for which the class mean was 70 with standard deviation 4. On which test did he do better relative to the rest of the class?

Respuesta :

Answer:

He did better on biology test.

Step-by-step explanation:

For comparing the scores we need to find z-scores for both subjects,

We know that,

z-score or standard score for x is,

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Where, [tex]\mu[/tex] is mean,

[tex]\sigma[/tex] is standard deviation,

In history test,

[tex]x=77[/tex]

[tex]\mu=70[/tex]

[tex]\sigma = 6[/tex]

Thus, the z-score would be,

[tex]z_1=\frac{77-70}{6}[/tex]

[tex]\approx 1.167[/tex]

In biology test,

[tex]x=79[/tex]

[tex]\mu = 70[/tex]

[tex]\sigma = 4[/tex],

Thus, the z-score would be,

[tex]z_2=\frac{79-70}{4}[/tex]

[tex]= 2.25[/tex]

∵ [tex]z_2>z_1[/tex]

Hence, he did better on biology test.

Otras preguntas