The time that a randomly chosen passenger waits for a local train between downtown Los Angeles station and St Diego station is uniformly distributed between 5 and 80 minutes. (a) Calculate the probability that a randomly chosen passenger’s waiting time is between 10 and 30 minutes. (b) Calculate the probability that the average waiting time of a random sample of 35 passengers is larger than 40 minutes. (c) Calculate the probability that the total waiting time of 3 passengers is larger than 30 minutes.
The time that a randomly chosen passenger waits for a local train between downtown Los Angeles station and St Diego station is uniformly distributed between 5 and 80 minutes.
(a) Calculate the
(b) Calculate the probability that the average waiting time of a random sample of 35 passengers is larger than 40 minutes.
(c) Calculate the probability that the total waiting time of 3 passengers is larger than 30 minutes.
(d) Show that the distribution of a sum of 3 uniform distributions like that in part (a) is not uniform.
(e) If there are two groups of 20 passengers each, one group waiting on the right-hand-side platform, and the other on the left-hand-side platform, what is the probability that the difference between the average waiting time of the two is larger than 5 minutes?
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