Question

Grades on an english test can be modeled as a normal distribution with mean 80 and standard deviation 5.

A) if the english department is awarding students with test grades in the top 5%, find the lowest grade a student needs to receive the award.

B) A student is randomly selected from the class so the distribution of this student's test grade is N(80,5), what is the probability that this student scored above a 90?

C) What is the probability that the student in part b scored exactly a 90?

D) If 5 students are randomly selected from the class. what is the probability that exactly 3 of them scored above a 90?

E) If 20 students are randomly selected from the class what is the probability that at least 12 of them scored above an 80?

Answer 1

(a)

(b)

(c)

Since normal distribution is continuous distribution so the probability exactly at one point is zero so the probability that the student in part b scored exactly a 90 is

P(X =90) = 0

(d)

Here we need to use binomial distribution with parameter n=5 and p=0.0228 (from part b). The  probability that exactly 3 of them scored above a 90 is

(e)

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Now we need to use binomial distribution with parameter n=20 and p=0.5. The  probability that at least 12 of them scored above an 80 is