Suppose your course grade depends on two test scores: X_1 and X_2. Each score is

Question

Suppose your course grade depends on two test scores: X_1 and X_2. Each score is a Gaussian (mu = 74, sigma = 16) random variable, independent of the other. (a) With equal weighting, grades are determined by Y = X_1/2 + X_2/2. An "A" grade requires Y greaterthanorequalto 90; what is P(A) = P(Y greaterthanorequalto 90)? Useful fact: the sum of two independent gaussian random variables is also a gaussian random variable. (b) A student proposes that only the better of the two exam scores M = max(X_1, X_2) should be used to determine the course grade. The professor agrees; what is P(A) = P(M greaterthanorequalto 90)? (c) In a class of 100 students, what is the expected increase in the number of A's awarded due to this change in policy?

Explanation / Answer

a) here mean of both grades =74

and std error of mean =16/(2)1/2 =11.3137

ehnce P(Y>90)=1-P(Y<90)=1-P(Z<(90-74)/11.3137)=1-P(Z<1.4142)=1-0.9214 =0.0786

b) probabilty that one grade is less then 90 =P(Y<90) =P(Z<1)=0.8413

hence probabilty that P(M>90) =P(at least one course has grade above 90) =1-P(none have ) =1-(0.8413)2 =0.2921

c) expected number to increase =(p(2)-P(1))*100 =(0.2921-0.0786)*100=21.35

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.