A bus is scheduled to arrive at the bus stop every morning at 8:00 A.M; however,...
A bus is scheduled to arrive at the bus stop every morning at 8:00 A.M; however, its arrival time is uniformly distributed between 7:55 A.M. and 8:05 A.M. The bus is considered to be on time if it is no more than 3 minutes early or 3 minutes late. Assuming that the bus arrivals are mutually independent for different days, give an approximation of the probability that out of 600 days, the bus is going to be on time more than 390 times. (Express your answer in terms of Φ, the cdf of the standard normal.)
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A bus is scheduled to arrive at the bus stop every morning at
8:00 A.M; however,...
In order to attend an important 8 A.M. lecture, you arrive at the shuttle stop at...
In order to attend an important 8 A.M. lecture, you arrive at the shuttle stop at a time distributed uniformly between 7:20 A.M. and 7:30 A.M. The time between consecutive shuttle arrivals is known to be exponentially distributed with mean 15 minutes. If the journey takes 30 minutes, what is the probability that you arrive late to the lecture?
The arrival time t(in minutes) of a bus at a bus stop is uniformly distributed between 10:00 A.M. and 10:03 A.M.
The arrival time t(in minutes) of a bus at a bus stop is uniformly distributed between 10:00 A.M. and 10:03 A.M. (a) Find the probability density function for the random variable t. (Let t-0 represent 10:00 A.M.) (b) Find the mean and standard deviation of the the arrival times. (Round your standard deviation to three decimal places.) (с) what is the probability that you will miss the bus if you amve at the bus stop at 10:02 A M ? Round your answer...
The time a bus will arrive is uniformly distributed from 8:00 AM until 8:20 AM. You...
The time a bus will arrive is uniformly distributed from 8:00 AM until 8:20 AM. You arrive at the bus stop at exactly 8:00 AM. What is the probability you will wait 12 minutes or more?
3. Buses arrive at a specified stop at 15-minute intervals starting at 7 A.M. That is,...
3. Buses arrive at a specified stop at 15-minute intervals starting at 7 A.M. That is, they arrive at 7, 7:15, 7:30, 7:45, and so on. If a passenger arrives at the stop at a time that is uniformly distributed between 7 and 7:40, find the probability that he waits more than 10 minutes for a bus.
4. You arrive at a bus stop at 10 o'clock, knowing that the bus will arrive...
4. You arrive at a bus stop at 10 o'clock, knowing that the bus will arrive at some time uniformly distributed between 10:00 and 10:30. (a) What is the probability that you will have to wait longer than 10 minutes? (b) If at 10:10 the bus has not yet arrived, what is the probability that you will have to wait at least an additional 2 minutes?
A person arrives at a bus stop each morning. The waiting time, in minutes, for a...
A person arrives at a bus stop each morning. The waiting time, in minutes, for a bus to arrive is uniformly distributed on the interval (0,15). a. What is the probability that the waiting time is less than 5 minutes? b. Suppose the waiting times on different mornings are independent. What is the probability that the waiting time is less than 5 minutes on exactly 4 of 10 mornings?
The bus arrives every 15 minutes starting at 8:00am and leaves immediately. You arrive at the...
The bus arrives every 15 minutes starting at 8:00am and leaves immediately. You arrive at the bus stop with a uniform distribution between 8:05am and 8:30am. Given that the bus arrival time and the time that you arrive at the bus stop are independent, what is the PDF of your wait time? Graph the PDF of your wait time.
The bus arrives every 15 minutes starting at 8:00am and leaves immediately. You arrive at the...
The bus arrives every 15 minutes starting at 8:00am and leaves
immediately. You arrive at the bus stop with a uniform distribution
between 8:05am and 8:30am and can be described as . Given that the bus arrival
time and the time that you arrive at the bus stop are independent,
what is the PDF of your
wait time?
fx(x) = {1/25, 0<x< 25 0, otherwise
The wait time (after a scheduled arrival time) in minutes for a train to arrive is...
The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0,12]. You observe the wait time for the next 95 95 trains to arrive. Assume wait times are independent Use the Normal approximation to the Binomial distribution (with continuity correction) to find the probability (to 2 decimal places) that 56 or more of the 95 wait times recorded exceed 5minutes
C. In Regular Bus City, there is a shuttle bus that goes between Stop A and Stop B, with no stops...
Question D
C. In Regular Bus City, there is a shuttle bus that goes between Stop A and Stop B, with no stops in between. The bus is perfectly punctual and arrives at Stop A at precise five minute intervals (6:00, 6:05, 6:10, 6:15, etc.) day and night, at which point it immediately picks up all passengers waiting. Citizens of Regular Bus City arrive at Stop A at Poisson random times, with an average of 5 passengers arriving every minute,...
3. Buses arrive at a specified stop at 15-minute intervals starting at 7 A.M. That is, they arrive at 7, 7:15, 7:30, 7:45, and so on. If a passenger arrives at the stop at a time that is uniformly distributed between 7 and 7:40, find the probability that he waits more than 10 minutes for a bus.
4. You arrive at a bus stop at 10 o'clock, knowing that the bus will arrive at some time uniformly distributed between 10:00 and 10:30. (a) What is the probability that you will have to wait longer than 10 minutes? (b) If at 10:10 the bus has not yet arrived, what is the probability that you will have to wait at least an additional 2 minutes?
The bus arrives every 15 minutes starting at 8:00am and leaves
immediately. You arrive at the bus stop with a uniform distribution
between 8:05am and 8:30am and can be described as . Given that the bus arrival
time and the time that you arrive at the bus stop are independent,
what is the PDF of your
wait time?
fx(x) = {1/25, 0<x< 25 0, otherwise
Question D
C. In Regular Bus City, there is a shuttle bus that goes between Stop A and Stop B, with no stops in between. The bus is perfectly punctual and arrives at Stop A at precise five minute intervals (6:00, 6:05, 6:10, 6:15, etc.) day and night, at which point it immediately picks up all passengers waiting. Citizens of Regular Bus City arrive at Stop A at Poisson random times, with an average of 5 passengers arriving every minute,...
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