Question

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

Answer 1

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,  $\mu_1 = 78$

And, standard deviation for class A, $\sigma_1 = 5$

Thus, the z-score for Class A,

$z_1 = \frac{x-\mu_1}{\sigma_1}$

$z_1 = \frac{87-78}{5}$ = 9/5 = 1.8

And, $z_1(1.8)=0.9641$

Also, mean for the class B is,  $\mu_2 = 76$

And, standard deviation for class B, $\sigma_2 = 4$

Thus, the z-score for Class B,

$z_2 = \frac{x-\mu_2}{\sigma_2}$

$z_2 = \frac{87-76}{4}$ = 11/4 = 2.75

$z_2(2.75)=0.9970$

Thus, $z_2 > z_1$

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