For each of the following, assume that a two-tailed test using the normal approximation to the binomial distribution with α = .05 is being used to evaluate the significance of the result.

a. For a multiple-choice test with 48 questions, each with 4 possible answers, how many would you have to get right to do significantly better than chance? That is, what X value is needed to produce a z-score greater than 1.96?

b. How many would you need to get right on a multiple-choice test with 192 questions to be significantly better than chance?

Remember that each X value corresponds to an interval with real limits. Be sure that the entire interval is in the critical region.