The Harbour Island Ferry leaves on the hour and at 15-minute intervals. The time, x, it takes John to drive from his house to the ferry has a uniform distribution with x between 10 and 20 minutes. One morning John leaves his house at precisely 8:00 A.M
a. What is the probability John will wait less than 5 minutes for the ferry?
b. What is the probability John will wait less than 10 minutes for the ferry?
c. What is the probability John will wait less than 15 minutes for the ferry?
d. What is the probability John will not have to wait for the ferry?
e. Suppose John leaves at 8:05 A.M. What is the probability John will wait (1) less than 5 minutes for the ferry; (2) less than 10 minutes for the ferry?
f. Suppose John leaves at 8:10 A.M. What is the probability John will wait (1) less than 5 minutes for the ferry; (2) less than 10 minutes for the ferry?
g. What appears to be the best time for John to leave home if he wishes to maximize the probability of waiting less than 10 minutes for the ferry?
a. .5
b. .5
c. 1
d. 0
e. (1) 0, (2) .5
f. (1) .5, (2) 1
g. 8:10
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