Question

A math teacher, wanting to assess students 'knowledge, put in a competition in which students' performance averaged 65 (with an excellent 100) and a standard deviation of 10 units. Let's consider that the distribution of performance is normal:
A. Find the probability that the performance of a randomly selected student is over 75.
B. If we consider that the random variable that describes student performance is continuous (that is, it can take any real value between 0 and 100 and not just integer values) find the probability that a student has a performance of exactly 72.
C. The principal wanted to give a score of "A" to 5% of students with the best performance and a score of "B" to the next 10% of (less) better students. What is the "base" for someone to get "A" and which one to get "B"?
D. Given your answer to sub-question (A), if we randomly select 4 students, what is the probability that at least 1 of them scored more than 75?

Answer 1