Two students in different classes took the same math test. Both students received a score of 87. In student A's class the mean was 78 and the standard deviation of 5. In student B's class the mean was 76 with a standard deviation of 4. Which student scored in the top 10% of their class?

A. student b
b. student a
C. both students
D. neither student

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parmesanchilliwack parmesanchilliwack · Answer 1 · 2018-12-21T13:06:15+01:00

Answer: Student B will score in the top of the class.

Step-by-step explanation:

Here both the students of class A and B scored 87.

Therefore, the value of random variable for both class is, x = 87

According to the question, mean for the class A is, [tex]\mu_1 = 78[/tex]

And, standard deviation for class A, [tex]\sigma_1 = 5[/tex]

Thus, the z-score for Class A,

[tex]z_1 = \frac{x-\mu_1}{\sigma_1}[/tex]

[tex]z_1 = \frac{87-78}{5}[/tex] = 9/5 = 1.8

And, [tex]z_1(1.8)=0.9641[/tex]

Also, mean for the class B is, [tex]\mu_2 = 76[/tex]

And, standard deviation for class B, [tex]\sigma_2 = 4[/tex]

Thus, the z-score for Class B,

[tex]z_2 = \frac{x-\mu_2}{\sigma_2}[/tex]

[tex]z_2 = \frac{87-76}{4}[/tex] = 11/4 = 2.75

[tex]z_2(2.75)=0.9970[/tex]

Thus, [tex]z_2 > z_1[/tex]

Therefore, student B scored in the top 10% of their class.