Let x be the number of courses for which a randomly selected student at a certai
ID: 3262566 • Letter: L
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.
It can be easily verified that = 4.66 and = 1.20.
(a) Because - = 3.46, 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 < - ) =
(b) What x values are more than 2 standard deviations away from the mean value (i.e., either less than - 2 or greater than + 2)? (Select all that apply.)
x = 1x = 2x = 4x = 5x = 6x = 7
What is the probability that x is more than 2 standard deviations away from its mean value?
P (x < - 2 or + 2 < x) =
Explanation / Answer
Answer to the question below:
a) P(X<4.66-1.2) = P(X<3.46) = P(Z< 3.46-4.66 / 1.2)
= P(Z<-1)
= .16
b) Mu +/- 2Sigma = 4.66 +/- 1.2 = 3.46 to 5.86
So, for value of x=1,2,3,6,7 we are more than 2 deviations away from mean
c) This probability is 1-.95 = .05 or 5%.
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