Question

A qualifying exam for a graduate school program has a math section and a verbal section. Students receive a score of 1, 2, or 3 on each section. Define X as a student’s score on the math section and Y as a student’s score on the verbal section. Test scores vary according to the following bivariate probability distribution.

			y
		1	2	3
	1	0.22	0.33	0.05
x	2	0.00	0.08	0.20
	3	0.07	0.05	0.00

μXX =   , and μYY =   

σXX =   , and σYY =   

The covariance of X and Y is ________ . The coefficient of correlation is _________ . The variables X and Y_______ independent.

The expected value of X + Y is_______ , and the variance of X + Y is ________________ .

To be accepted to a particular graduate school program, a student must have a combined score of 4 on the qualifying exam.

What is the probability that a randomly selected exam taker qualifies for the program?

0.46

0.33

0.47

0.45

Chebysheff’s Theorem states that the proportion of observations in any population that lie within k standard deviations of the mean is at least 1 – 1 / k² (for k > 1).

According to Chebysheff’s Theorem, there is at least a 0.75 probability that a randomly selected exam taker has a combined score between_______ and_______ .

Answer 1

According to Chebysheff’s Theorem, there is at least a 0.75 probability that a randomly selected exam taker has a combined score between 3.48-2*1.0907=1.2986 and 3.48+2*1.0907=5.6614.