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 p(x) 0.02 0.04 0.09 0.24 0.39 0.17 0.05 It can be easily verified that = 4.65 and = 1.24. 3.41, the x values 1, 2, and 3 are more than 1 standard deviation below the mean what is the probability that ris more than 1 standard deviation below a Because mean? S b) what x values are more than 2 standard deviations away from the mean value either less than 20 or greater than 20 Select all that apple x=3 (c) What is the probability that x is more than 2 standard deviations away from its mean value?

Explanation / Answer

= 4.65

= 1.24

(a) P ( x < - ) = P(X < 3.41) = P(1) + P(2) + P(3) = 0.02 + 0.04 + 0.09 = 0.15

(b) Here Limits +- 2 = 4.65 +- 2 * 1.24 = (2.17, 7.13)

so there are two value x = 1 and x = 2 are outside the 2 standard deviation away.

(c) P (X < - 2 and X > + 2) = Pr( X = 1) + Pr( X = 2) = 0.02 + 0.04 = 0.06

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