Chapter 11, Problem 31E

To determine

To find: The average size of the family is and assumes that girls and boys are equally likely.

Explanation of Solution

It is required to find the average size of a family and it can use the following steps to simulate it:

Step 1

The component is the individual child. 

 Step 2 

It is required to produce random digits from 0 to 9 for simulation. Let 0-4 represent a boy and 5-9 represent a female, and once a child of each gender is simulated, the trial consists of generating random digits.

 Step 3

The responsible variable is the number of children simulated on girls and up to one kid.

 Step 4

At least 10 trials need to be run in the simulation process and each trial consists of generating random digits before a child of each gender is simulated. By using random number generators, it produces random numbers using the steps below:

1) As per our needs, add random numbers.

2) Depends on random digits between 0 and 9

3) Press the Submit key.

Trial Number	Component Outcomes	Trial Outcomes
1	92	2
2	145	3
3	84	2
4	478	3
5	7451245	7
6	71	2
7	4574	4
8	684	3
9	14	2
10	65	2
Total		30

Let a boy get 0-4 random digits and a girl get 5-9 random digits. The first random digit 9, for instance, means female, and the second random digit 2 is for a kid, giving the total number of results for trial number 1 is 2 and so on up to 10 trial numbers.

 Step 5

It is required to find the average family size simulated by:

  $\begin{array}{c}Averagefamily\text{}Size\text{}\text{}\text{}\text{}\text{}\text{}=\frac{totalnumberofdigitgeneratedineachtrials}{totalnumberoftrials}\\ =\frac{30}{10}\\ =3\end{array}$

The average size of the family is 3.

Step 6

Based on the simulation, it can conclude that the expected number children in average size of the family are 3.

The average family size is 3.

 Step 6

On the basis of the simulation, it can infer that 3 is the predicted number of children in the family's average size.