Let x be the number of courses for which a randomly selected student at a certai

Question

Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the following table.

a) what id the probaility that the selected student is taking at most five courses?

b) what is the mean of x?

c) what is the standard deviation?

d) what is the probaility that the selected student is registered for a number of courses that is withing one standatrds deviation of the mean?

please show full work.

Explanation / Answer

a)

probaility that the selected student is taking at most five courses = P(1)+P(2)+P(3)+P(4)+P(5)

= 0.02+0.03+0.09+0.25+0.40 = 0.79

b)

mean of x = 1*0.02+2*0.03+3*0.09+4*0.25+5*0.40+6*0.16+7*0.05 = 4.66

b)

variance

= (1-4.66)2*0.02+(2-4.66)2*0.03+(3-4.66)2*0.09+(4-4.66)2*0.25+(5-4.66)2*0.40+(6-4.66)2*0.16+(7-4.66)2*0.05

= 1.4444

standard deviation = variance = 1.444 = 1.2018

d)

interval for for one standatrds deviation of the mean is (4.66-1.2018, 4.66+1.2018) i.e (3.5,5.9)

values in this interaval are 4,5

probaility that the selected student is registered for a number of courses that is withing one standatrds deviation of the mean = P(4)+P(5) = 0.25+0.4 = 0.65

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