Let x be the amount of time (in minutes) that a particular San Francisco commute
ID: 3221080 • Letter: L
Question
Let x be the amount of time (in minutes) that a particular San Francisco commuter must wait for a BART train. Suppose that the density curve is as pictured below (a uniform distribution):
(a) What is the probability that x is less than 10 min? more than 14 min?
P (x is less than 10 minutes) =
P (x is more than 14 minutes) =
(b) What is the probability that x is between 7 and 13 min?
P (x is between 7 and 13 minutes) =
(c) Find the value c for which P(x < c) = .7.
c = mins
Explanation / Answer
Given,
X ~ U(0, 20)
a) P(X < 10)
= (10 - 0) / (20 - 0)
= 10 / 20
= 0.5
P(X > 14)
= (20 - 14) / (20 - 0)
= 6 / 20
= 0.3
b) P(7 < X < 13)
= (13 - 7) / (20 - 0)
= 6 / 20
= 0.3
c) P(x < c) = 0.7
(c - 0) / (20 - 0) = 0.7
c / 20 = 0.7
c = 20(0.7)
c = 14 min
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