Question

1. 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?
2. The scores on a final exam were approximately normally with a mean of 82 and standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?

Answer 1

Answer:

1. Student B scored in the top 10% of his class.

2. 2 students failed the exam.

Step-by-step explanation:

1. We have been given that two students in different classes took the same math test.

First of all let us find z-score for student A and B using z-score formula.

$z=\frac{x-\mu}{\sigma}$, where,

$z=\text{z-score}$,

$x=\text{Raw-score}$,

$\mu=\text{Mean}$,

$\sigma=\text{Standard deviation}$.

$\text{z-score for student A}=\frac{87-78}{5}$

$\text{z-score for student A}=\frac{9}{5}$

$\text{z-score for student A}=1.8$

$\text{z-score for student B}=\frac{87-76}{4}$

$\text{z-score for student B}=\frac{11}{4}$

$\text{z-score for student B}=2.75$

Now let us find the probability that corresponds to z-score of both students using normal distribution table.        

$P(z$

$P(z$      

Since probability of z-score of student B is greater than student A, therefore, student B scored in the top 10% of his class.

2. We have been given that the scores on a final exam were approximately normally with a mean of 82 and standard deviation of 11.

First of all let us find z-score corresponding to raw score 60.

$z=\frac{60-82}{11}$

$z=\frac{-22}{11}$

$z=-2$

Now we will find the probability of z-score -2 using normal distribution table.

$P(z$

Therefore, the probability that a randomly student will score below 60 scores is 0.02275.

To find the number of students, who will fail the exam, let us multiply 0.02275 by 85.

$\text{The number of students, who failed the exam}=0.02275\times 85$

$\text{The number of students, who failed the exam}=1.93375\approx 2$

Therefore, 2 students failed the exam.

Answer 2

All of them passed except 4 of them.