The probability distribution function, PDF, for the number of hours of sleep a s
ID: 3181497 • Letter: T
Question
The probability distribution function, PDF, for the number of hours of sleep a student gets the night before a final exam is given in the following table:
X
P(X)
1
.02
2
.01
3
.03
4
.03
5
.15
6
.35
7
.20
8
.18
9
.03
What is the probability a randomly chosen student gets, exactly, a "full eight hours" of sleep the night before the exam?
What is the probability a randomly chosen student gets four or less hours of sleep the night before an exam?
What is the probability a randomly chosen student gets seven or more hours of sleep the night before an exam?
Not sure how to get these answers...
X
P(X)
1
.02
2
.01
3
.03
4
.03
5
.15
6
.35
7
.20
8
.18
9
.03
Explanation / Answer
a) P(X = 8) = 0.18
b) P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= 0.02 + 0.01 + 0.03 + 0.03
= 0.09
c) P(X > 7) = P(X = 7) + P(X = 8) + P(X = 9)
= 0.20 + 0.18 + 0.03
= 0.41
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