Question

A mark of at least 50 is required to pass a course. The marks this year run from a low of 45 to a high of 83, with a mean of 64 and a standard deviation of 5.The professor would like all students to pass, so he adjusts the marks to achieve a mean of 72 with the standard deviation of 5. Is this enough to ensure that all students will pass?

Answer 1

Ans - This will insure that all student pass.

Explanation : Required mark to pass = 50.

Marks this year ranges from 45 to 83. Let X1, X2, X3,...Xn be the marks of n students then min Xi = 45 and max Xi = 83

Now suppose the new marks are Yi = a + bXi

Then Var(Y) = b2*Var(X) = b2*5

Given that variance of the adjusted marks = 5, hence b2*5 = 5 hence b = 1

and E(Y) = a + bE(X) = a + b*64, hence since b = 1, so 72 = a + 64

Hence a = 8,

So essentially professor increased every student's marks by 8, so the minimum reaches 45 + 8 = 53.

Since the student with least score passes the course, so does all students.