The first thing we do is we notice it's a one-sided test--that is, if this drug was even better
than advertised we're not really that concerned, to be honest.
Then we graph the binomial just like before.
Here are the outcomes and here are the probabilities.
Obviously, 8 is the most likely outcome, assuming the null hypothesis is correct.
The critical region is not defined from the left side,
which is fewer people are healthy and the treatment doesn't work as well as advertised.
Let's add up until we reach 0.05, which is right over here.
The sum happens to be 0.032, which is below 5%. So 5 is the correct answer over here.