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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 9, Problem 55RE

Textbook Problem

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**Transportation** The arrival time *t* (in minutes) of a train at a train station is uniformly distributed between 7:00

(a) Find the probability density function for the random variable *t.*

(b) Find the mean and standard deviation of the arrival time.

(c) What is the probability that you will miss the train if you arrive at the train station at 7:04

**(a)**

To determine

**To calculate:** The probability density function for the random variable *t* which is the arrival time (in minutes) of a train at a station which is uniformly distributed between

**Given Information:**

The arrival time of a train *t* (in minutes) is uniformly distributed between

**Formula used:**

The probability density function of uniform probability distribution is defined as,

**Calculation:**

Consider the given information,

Use the definition of uniform probability density function

**(b)**

To determine

**To calculate:** The mean and standard deviation of the arrival time *t* (in minutes) of a train at a station which is uniformly distributed between

**(c)**

To determine

**To calculate:** The probability of missing the train if the arrival at the station is at *t* (in minutes) uniformly distributed between

Calculus: An Applied Approach (MindTap Course List)

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