A distribution of grades in an introductory statistics course (where A = 4, B =

Question

A distribution of grades in an introductory statistics course (where A = 4, B = 3, etc) is:

part a: Find the probability that a student has passed this class with at least a C (the student's grade is at least a 2).

part b: Find the probability that a student has an A (4) given that he has passed the class with at least a C.

part c: Find the expected grade in this class.

part d: find the variance and standard deviation for the class grades.

part e: Suppose a student knows he/she has passed the course with a C, what should they expect their grade to be?

I'm interested in how I would go about finding the answer to this problem! What steps should I take? I already know the answer, but I just want to know how we reach it in a clear and concise manner! Thank you!

Explanation / Answer

a) P(X > 2) = P(X = 2) + P(X = 3) + P(X = 4)

                   = 0.2 + 0.32 + 0.19

                   = 0.71

b) P(X = 4 | X > 2) = P(X = 4) / P(X > 2)

                              = 0.19 / 0.71

                              = 0.268

c) E(X) = 0 * 0.11 + 1 * 0.18 + 2 * 0.2 + 3 * 0.32 + 4 * 0.19

             = 2.3

d) E(X2) = 02 * 0.11 + 12 * 0.18 + 22 * 0.2 + 32 * 0.32 + 42 * 0.19

              = 6.9

Var(X) = E(X2) - (E(X))2

           = 6.9 - 2.32

           = 1.61

standard deviation = sqrt(1.61) = 1.27

e) Expected grade is 2

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