There are two separate issues here:
1. The word 'everybody' : this is a singular noun.
We say 'Everybody is...' and 'Everybody knows..' and 'Everybody has'. This is why your answer is wrong : it should be 'Everybody HAS stated..', not 'have'. Of course, if a past simple is used, this mistake doesn't arise - if you say 'Everybody stated', this is fine, too.
2. The pronoun used with impersonal or non-gender-specific nouns.
There are several options here:
Your option, 'his/her', is fine.
You could also use 'his or her'.
The very outdated masculine-only form still exists ( just 'his'), but it is very rare nowadays.
The best option in modern English is the singular 'their'.