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?

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.

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