Cars arrive at a tollbooth at a mean rate of 10 cars every 20 minuts according to a Poisson process. Let X = the waiting time in minutes until the 25th toll is collected. a. How is X distributed? b. Base on the answer to a. above, write the complete pdf of X. c. Find the probability that the tollbooth collector has to wait more than 63.15 minutes to collect the 25th toll?

Cars arrive at a tollbooth at a mean rate of 10 cars every 20 minuts according to a Poisson process. Let X = the waiting time in minutes until the 25th toll is collected. a. How is X distributed? b. Base on the answer to a. above, write the complete pdf of X. c. Find the probability that the tollbooth collector has to wait more than 63.15 minutes to collect the 25th toll?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Question

Cars arrive at a tollbooth at a mean rate of 10 cars every 20 minuts according to a Poisson process. Let X = the waiting time in minutes until the 25th toll is collected.

a. How is X distributed?

b. Base on the answer to a. above, write the complete pdf of X.

c. Find the probability that the tollbooth collector has to wait more than 63.15 minutes to collect the 25th toll?

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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