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

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.

It can be easily verified that = 4.68 and = 1.17.

(a) Because = 3.51, the x values 1, 2, and 3 are more than 1 standard deviation below the mean. What is the probability that x is more than 1 standard deviation below its mean?
P(x < ) =  

(c) What is the probability that x is more than 2 standard deviations away from its mean value?
P(x < 2 or + 2 < x) =

Solution

a)

P(x < 3.51) = P(1) + P(2) + P(3)

= 0.02 + 0.02 + 0.09

= 0.13 [ANSWER]

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c)

As

u - 2*sigma = 4.68 - 2*1.17 = 2.34
u + 2*sigma = 4.68 + 2*1.17 = 7.02

Thus,

P(x<2.34 or x>7.02) = P(1) + P(2) = 0.02 + 0.02 = 0.04 [ANSWER]