Let X be the random variablenumber of people who worked on their home-based businesses for 35 hours or more.

Then X ~ Binomial(n = 800, p = 0.293)

30.5% of 800 is equal to 244.

So you want Pr(X \geq 244).

It'd be reasonable to use the normal approximation to the binomial distribution here (why?). But why bother if you can access a standard machine like a TI-89 that can crank out an answer in short order.