5. Suppose that a person commutes to work by bus. The person arrives at the bus...

Question

Question

5. Suppose that a person commutes to work by bus. The person arrives at the bus stop at the same time every day. The waiting

Answer 1

Answer #1

5)

here for uniform distribution parameter a(5 minute) =300 sec and b(10 minutes)=600 (seconds)

a)P(between 5 min and 15 seconds (315 seconds) and 7 minutes and 30 seconds (450 seconds):

probability =

P(315<X<450)=

(450-315)/(600-300)=

0.4500

b)

P(wait more than 7 minute 45 seconds (465 seconds)

probability =

P(X>465)=

1-P(X<465)=

1-(465-300)/(600-300)=

0.4500

Add a comment

Answer 2

Similar Homework Help Questions

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?
A bus comes by every 13 minutes. The times from when a person arives at the...

A bus comes by every 13 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 13 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is ? c. The probability that the person will wait more than 7 minutes is ? d. Suppose that the...
A bus arrives every 11 minutes to a stop. The waiting time for a particular individual...

A bus arrives every 11 minutes to a stop. The waiting time for a particular individual is assumed to be a random variable with uniform continuous distribution. What is the probability that the individual waits for more than 6 minutes? Answer using 4 decimals.

Currently the bus runs every 7 minutes during the day. Let X represent the amount of...

Currently the bus runs every 7 minutes during the day. Let X represent the amount of time Sofia waits for the bus, assuming she arrives at the bus stop at a random time and the bus is running on schedule. (That is, the amount of time Sofia waits is uniformly distributed.) Find the following probabilities (use 2 decimal places for all answers): (a) The probability Sofia waits at most 2 minute(s) = (b) The probability Sofia waits less than 2...
A bus comes by every 15 minutes. The times from when a person arives at the...

A bus comes by every 15 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 15 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the person will wait more than 5 minutes is d. Suppose that the person has...
For a passenger who arrives at a certain bus stop at a random moment in time,...

For a passenger who arrives at a certain bus stop at a random moment in time, the time spent waiting for the bus is uniformly distributed from 0 to 9 minutes. What is the probability someone who arrives at this bus stop at a random moment will wait at least 7 minutes for the bus? (Round to the nearest tenth of a percent.)

A bus comes by every 14 minutes. The times from when a person arives at the...

A bus comes by every 14 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 14 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. c. The probability that the person will wait more than 4 minutes is _____ d. Suppose that the person has already been waiting for 0.5 minutes. Find the probability that the...
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.
2. The University of Southwest Arizona provides bus transportation services to students while they are on...

2. The University of Southwest Arizona provides bus transportation services to students while they are on campus. A bus arrives at the North Main Street and College Drive stop every 30 minutes, between 6 in the morning and 11 at night during the week. Students arrive at the stop at random times. The time a student waits has a uniform distribution of 0 to 30 minutes. A. Draw a graph of the distribution. B. Show that the area of this...

2. The 46A bus leaves the terminus every 10 minutes exactly. For this reason, for any individual who arrives at a bus s...

2. The 46A bus leaves the terminus every 10 minutes exactly. For this reason, for any individual who arrives at a bus stop on the route, his minimum waiting time is 0 minutes and his maximum waiting time is 10 minutes, and between these two times, all possible waiting times are equally likely. Write down the probability density function for waiting times on the bus route and draw the distribution. What is the expected waiting time? What is the standard...