Question

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between

0

and

7

minutes. Find the probability that a randomly selected passenger has a waiting time

greater than

1.25

minutes.

Find the probability that a randomly selected passenger has a waiting time

greater than

1.25

minutes.

Answer 1

Concepts and reason

A uniform distribution is known as continuous uniform distribution or rectangular distribution. The range of this distribution is defined by two parameters ‘a’ and ‘b’ which are its minimum and maximum values respectively.

Fundamentals

The probability distribution function for the Uniform distribution is given by,

The formula for mean, variance, and probability are as follows:

Where,

$\begin{array}{c}\\a = {\rm{ minimum}}\\\\b = {\rm{maximum}}\\\\d = {\rm{upper bound }}\\\\c = {\rm{lower bound}}\\\end{array}$

The cumulative probability distribution function of X is defined as,

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 7 minutes.

The probability distribution function is given by,

Therefore, the probability distribution function of the arrival of passengers is given by,

Compute the probability that a randomly selected passenger has a waiting time greater than 1.25. That is

Ans:

The probability that a randomly selected passenger has a waiting time greater than 1.25 is 0.8214.