A city bus runs every 6 minutes on a certain route. Let X be the waiting time of a passenger arriving at a random time to a bus stop. 1. Describe the distribution of X: ₁b-6 2. Use the random variable notation to express symbolically each of the following: P(X<3) The probability of an event in which the waiting time of a randomly selected passenger is less than 3. ✓An event in which the waiting time of a randomly selected passenger is less X<2 than 2. X-U P(X<5)=0.83 The probability of an event in which the waiting time of a randomly selected passenger is less than 5 is equal to 0.83. 3. Use the above probability density curve to find the probability that it takes: i. less than 2 minutes to wait for the bus? (a=0 ii. more than 3 minutes to wait for the bus? 0.33 (round the answer to 2 decimal places) 4. Find the 55-th percentile: iii. between 3 and 4 minutes to wait for the bus? I 55% 0.33x (round the answer to 2 decimal places) 0.17 iv. more than 7 minutes to wait for the bus? 0.00 (round the answer to 2 decimal places) v. less than 13 minutes to wait for the bus? 1.00 (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places)
A city bus runs every 6 minutes on a certain route. Let X be the waiting time of a passenger arriving at a random time to a bus stop. 1. Describe the distribution of X: ₁b-6 2. Use the random variable notation to express symbolically each of the following: P(X<3) The probability of an event in which the waiting time of a randomly selected passenger is less than 3. ✓An event in which the waiting time of a randomly selected passenger is less X<2 than 2. X-U P(X<5)=0.83 The probability of an event in which the waiting time of a randomly selected passenger is less than 5 is equal to 0.83. 3. Use the above probability density curve to find the probability that it takes: i. less than 2 minutes to wait for the bus? (a=0 ii. more than 3 minutes to wait for the bus? 0.33 (round the answer to 2 decimal places) 4. Find the 55-th percentile: iii. between 3 and 4 minutes to wait for the bus? I 55% 0.33x (round the answer to 2 decimal places) 0.17 iv. more than 7 minutes to wait for the bus? 0.00 (round the answer to 2 decimal places) v. less than 13 minutes to wait for the bus? 1.00 (round the answer to 2 decimal places) (round the answer to 2 decimal places) (round the answer to 2 decimal places)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 6
A city bus runs every 6 minutes on a certain route. Let X be the waiting time of a passenger arriving at a
random time to a bus stop.
1. Describe the distribution of X:
✓₁b-6
2. Use the random variable notation to express symbolically each of the following:
P(X<3) ✓ The probability of an event in which the waiting time of a randomly selected
passenger is less than 3.
✓ An event in which the waiting time of a randomly selected passenger is less
X<2
than 2.
X~ U✓
P(X<5)=0.83 The probability of an event in which the waiting time of a randomly selected
passenger is less than 5 is equal to 0.83.
3. Use the above probability density curve to find the probability that it takes:
i. less than 2 minutes to wait for the bus?
(a=0
ii. more than 3 minutes to wait for the bus?
0.33 (round the answer to 2 decimal places)
4. Find the 55-th percentile:
iii. between 3 and 4 minutes to wait for the bus?
I 55%
0.33x (round the answer to 2 decimal places)
0.17
iv. more than 7 minutes to wait for the bus?
(round the answer to 2 decimal places)
0.00
v. less than 13 minutes to wait for the bus?
1.00
(round the answer to 2 decimal places)
(round the answer to 2 decimal places)
(round the answer to 2 decimal places)
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