$\phi$ is a 3SAT CNF formula. All variables in each clause of $\phi$ are distinct. The expected number of satisfied clauses under the uniform random assignment is given as $\frac{7m}{8}$. A satisfying assignment of the CNF means that all $m$ clauses must be true. (A CNF is defined as a conjunction of disjunction of literals.)
We know that if $m < 8$, then that means $E(X) < 7$. I don't understand how this suggests the existence of at least one satisfying assignment.
Hints will be appreciated, thank you!