Answer
a) Greater than $20$
b) $24$
c) Using the equation for mean we derive the answer in part b)
Work Step by Step
a) The number of people attended in the first and the third meeting is less than $20$. The attendance of the second meeting is $21$. As the majority of the attendance is less than $20$, the mean of these $3$ numbers will be less than $20$. For the mean to increase to $20$, the attendance of the fourth meeting should be greater than $20$.
b) The number of people who attended the first meeting is $2$ less than the average, while that of the third meeting is $3$ less than average. Collectively, this is $5$ less than the average.
For the second meeting, we have $1$ attendance greater than the average. To meet the $5$ lesser than average, we need $4$ more attendance. Hence, the attendance of the fourth meeting can be estimated to $24$.
c) The equation for the mean is $$\text{mean} = \frac{\text{total attendance of all meetings}}{\text{total number of meetings}}.$$ Let's note the attendance of the fourth meeting by $x$. Then we have
$$\begin{align}
20&= \dfrac{18+21+17+x}{4}\\
20& = \dfrac{56 + x}{4}\\
80&= 56 + x \text{ (multiplying by 4 throughout)}\\
24& = x \text{ (subtracting 56 from both sides)}.
\end{align}$$
Therefore we have confirmed that the estimate made in part b) is correct.
