C++ for Engineers and Scientists
C++ for Engineers and Scientists
4th Edition
ISBN: 9781133187844
Author: Bronson, Gary J.
Publisher: Course Technology Ptr
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Chapter 5, Problem 1PP

(Probability) The probability that a phone call will last less than t minutes can be pproximated by the exponential probability function:

Probability that a call lasts less than t m i n u t e s   =   1     e   t / a

a   i s   t h e   a v e r a g e   c a l l   l e n g t h . e   i s   E u l e r s   n u m b e r   ( 2.71828 ) .

For example, assuming the average call length is 2 minutes, the probability that a call will last

less than 1 minute is calculated as 1     e 1 / 2   =   0.3297. Using this probability equation, write a

C++ program that calculates and displays a list of probabilities of a call lasting less than 1 minute to less than 10 minutes, in 1-minute increments.

Expert Solution & Answer
Check Mark
Program Plan Intro

Program plan:

  • Include the header files and using the namespace for standard I/O.
  • Define the main function.
  • Declare the variables x and z of integer type and y of double data type.
  • Declare the essential variables.
  • Use the loop to iterate.
  • Calculate the probability that the call last less than t minutes.
  • Display the list of probabilities in tabular format

Program description:

The main purpose of the program is to calculate theprobability of that a call will last less than one minute. This is calculated by the below formula: -

  p=1etaeistheEuler'snumber(2.71828)aistheaveragecalllengthtistheminutes

Explanation of Solution

Program:

//Importing the essential headers
#include <iostream>
#include <iomanip>
#include <math.h>
//Using the namespace for standard I/O
usingnamespacestd;
//Defining the main function
intmain()
{
//Declaring the essential variables 
double p;//to store the Probability
double e =2.71828;//to store the Euler’s number
int a=2;//to store the average call length
cout<<"Call Time\tProbability\n";
//Using the loop to iterate 
for(int t =1; t <10; t++)
{
//Calculating the probability that the call last less than t minutes
        p =1-pow(e,(-1*t)/(a));
//Displaying the list of probabilities in tabular format 
cout<<setprecision(0)<< fixed << t <<"\t\t"<<setprecision(4)<< p <<endl;
}
}

Sample output:

C++ for Engineers and Scientists, Chapter 5, Problem 1PP

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