Question

In a randomized trial, 200 subjects were to be randomly assigned either to the drug treatment group or to the placebo group. Researchers flipped a coin to decide each participant’s treatment assignment. After randomization, 112 subjects were in the treatment group and 88 were in the control group. What’s the probability that 112 or more subjects could end up in the treatment group purely by chance? Hint: use a normal approximation to the binomial.