Chapter 1.2, Problem 50E

(a)

To determine

To find:the number of students who attended the fourth meeting greater than or less than $20$ .

Answer to Problem 50E

Greater than $20$ for the first $3$ meeting, $2$ meeting had less than $20$ people so, the other $2$ meetings must have more than $20$ people in order for the average to be $20$ .

Explanation of Solution

Given:

The mean attendance for the first four meetings is $20$ .

Concept used:

Arithmetic mean:

Mean: $\stackrel{-}{x}=\frac{{\displaystyle \sum xi}}{N}$ .

Calculation:

from the given graph it is clear that:

Greater than $20$ for the first $3$ meeting, $2$ meeting had less than $20$ people so, the other $2$ meetings must have more than $20$ people in order for the average to be $20$ .

Hence,Greater than $20$ for the first $3$ meeting, $2$ meeting had less than $20$ people so, the other $2$ meetings must have more than $20$ people in order for the average to be $20$ .

(b)

To determine

To find:the estimation number of students who attended the fourth meeting.

Answer to Problem 50E

In order to have an average of $20$ , the fourth meeting needs to have $4$ more than $20$ people in order to make the differences equal to $0$ .

Explanation of Solution

Given:

Concept used:

Arithmetic mean:

Mean: $\stackrel{-}{x}=\frac{{\displaystyle \sum xi}}{N}$ .

Calculation:

About $24$ people. The first meeting had $2$ less than $20$ people, the second meeting had $1$ more than $20$ people and the third meeting had $3$ less than $20$ people.

  $-2+1-3=-4.$

Hence, In order to have an average of $20$ , the fourth meeting needs to have $4$ more than $20$ people in order to make the differences equal to $0$ .

(c)

To determine

To find:the description of ways that can check the estimate in part b.

Answer to Problem 50E

  $x=24$ .

Explanation of Solution

Given:

Concept used:

Arithmetic mean:

Mean: $\stackrel{-}{x}=\frac{{\displaystyle \sum xi}}{N}$ .

Calculation:

It can be written and solve an equation to check the estimation as:

  $\begin{array}{l}\frac{18+21+17+x}{4}=20.\\ 18+21+17+x=80.\\ x=24.\end{array}$

Hence, $x=24$ .