1. A statistics professor classifies his students according to their grade point average (GPA) and their...

1. A statistics professor classifies his students according to their grade point average (GPA) and their class rank. GPA is on a 0.0 – 4.0 scale, and class rank is defined as the lower class (year 1 and year 2) and the upper class (year 3 and year 4). One student is selected at random.

	GPA
	Under 20	2.0 -3.0	over 3.0
Lower Class (Year 1 and 2)	0.05	0.20	0.10	0.35
Upper Class (Year 3 and 4)	0.10	0.35	0.20	0.65
	0.15	0.55	0.30	1

a. Given that the student selected is in the upper class (year 3 and 4), what is the probability that her GPA over 3.0?

b. What is the probability that the student is in the upper class (year 3 and 4) or having a GPA over 3.0?

c. Are being in the upper class (year 3 and 4) and having a GPA over 3.0 independent? Prove statistically.

d. Are being in the upper class (year 3 and 4) and having a GPA over 3.0 mutually exclusive? Prove statistically.

Expert Solution

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orchestra answered 1 year ago

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