Answer
33 high school students.
Work Step by Step
The probability that the sample contains at least 12 is the complement of the probability that the sample contains fewer than 12.
$P(fewer~than~12)=1-P(at~least~12)=1-0.99=0.01$
Now, try to guess the value of $n$ using excel:
- $n=30$: "=BINOMDIST(11;30;0.55;TRUE)" $=0,0334\gt0.01$
- $n=31$: "=BINOMDIST(11;31;0.55;TRUE)" $=0,0227\gt0.01$
- $n=32$: "=BINOMDIST(11;32;0.55;TRUE)" $=0,0151\gt0.01$
- $n=33$: "=BINOMDIST(11;33;0.55;TRUE)" $=0,00998\lt0.01$
If $P(fewer~than~12)\lt0.01$, then $P(at~least~12)\gt0.99$
