Answer
170.
Work Step by Step
We need to achieve that $P(X\geq24)\geq0.98$, let's check when the equality is true. $P(X\geq24)=1-\sum_{x=0}^{23}{n \choose x}\cdot 0.2^x \cdot 0.8^{n-x}=0.98$, and we are looking for the n this is true for. n=170 satisfies the equation, this is the minimum number of integrated circus boards.
