Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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

Density 0.05 20 Minutes

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