Question

The GPA of graduating engineering students in the fictitious Kingdom of Statistans approximately normally distributed with a mean of 3.1 and a standard deviation of 0.2. The starting salary in Statistan is decided by the central government to be exactly $35K + $2.5K times the square of the GPA.

(a) What GPAs and salaries do the top 20% of graduating students have?

(b) What are the expected value and standard dev. of the starting salary?

(c) What’s the ranking of a graduating student who has a starting salary of $58K, i.e., what fraction of students have a higher starting salary?

Answer 1

Let X denote the GPA of the student. Then,

Let Y denote the salary of the student. Then Y = 35000 + 2500X²

a)

We want to find 'x' such that P(X>x) = 0.2

which is the minimum GPA for top 20% of graduating students.

So, salary for top 20% of graduating students = 35000 + 2500(3.26832)² = $61704.78906

b)

The starting salary is given by:Y = 35000 + 2500X²

^So,

Now,

So,

c)

If Y=58000, then 58000 = 35000 + 2500X²

^{On solving, we get, x = 3.0332}

^Now,

^{which means that 62.93%} students have a higher starting salary than $58000.