Consider the information on the MENT test given in the previous exercise.

a. The exact binomial probability of a score of 42 or less for someone who is not faking the test (p = 0.96) is

p(x ≤ 42) = 0.000000000013

Explain why this probability was calculated using the binomial formula rather than using a normal approximation.

b. The authors of the study described in the previous exercise propose that someone who scores 42 or less on the MENT exam is faking the test. Explain why this is reasonable, using the probability from Part (a) and the probabilities from the previous exercise as justification.