A distribution of grades in an introductory statistics course (where A - 4, B-3,

Question

A distribution of grades in an introductory statistics course (where A - 4, B-3, ete) is: 0 3 4 POX) 0.1 0.17 0.2 0.32 0.2 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 (2) Part e: Find the expected grade in this class. d standard deviation a student knows he/she has passed the course with a C, what should they expect BONUS: Suppose their grade to be?

Explanation / Answer

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).
P(the student’s grade is at least a 2) = P(2) + P(3) + P(4) = 0.21 + 0.32 + 0.2 = 0.73

Part B: Find the probability that a student has an A (4) given that he has passed the class with at least
C(2).

P( probability that a student has an 4) = 0.2
P(a student has an 4 | the student’s grade is at least a 2 ) = P( a student has an 4 ) n p( the student’s grade is at least a 2) / p( the student’s grade is at least a 2)
= 0.2 / 0.73 = 0.27397

Part C: Find the expected grade in this class.

f= 1

fx = 2.35

Mean = fx / f = 2.35

Part d: Find the variance and standard deviation for the class grades.

Mean square = f x^2 / f = 7.09

Variance = (Mean square) - (Mean)^2

Variance = f x^2 - Mean^2 = 1.568

Stadard Dev= Var = 1.252

Values ( X ) Frequency(f) fx ( X^2) f x^2 0 0.1 0 0 0 1 0.17 0.2 1 0.17 2 0.21 0.4 4 0.84 3 0.32 1 9 2.88 4 0.2 0.8 16 3.2

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