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? 0.45 0.47 0.46 0.33 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 .

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 19SGR

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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?

0.45

0.47

0.46

0.33

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 .

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