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.
, where,
,
,
,
.
Now let us find the probability that corresponds to z-score of both students using normal distribution table.
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.
Now we will find the probability of z-score -2 using normal distribution table.
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.
Therefore, 2 students failed the exam.