In a certain population, 11% of people are left-handed. Suppose that you plan to randomly select 100 people and ask each person whether they are left handed. Suppose that in calculating each of the probabilities below, you use the normal distribution as an approximation to the binomial but that you fail to use a continuity correction. In which cases will you obtain an answer that is too large?
A: the probability that among the 100 people, at least 12 are left-handed
B: the probability that among the 100 people, more than 12 are left-handed
C: the probability that among the 100 people, between 10 and 14 inclusive are left-handed
A)A and C
B)B and C
C)A only
D)B only

Question

In a certain population, 11% of people are left-handed. Suppose that you plan to randomly select 100 people and ask each person whether they are left handed. Suppose that in calculating each of the probabilities below, you use the normal distribution as an approximation to the binomial but that you fail to use a continuity correction. In which cases will you obtain an answer that is too large? 
A: the probability that among the 100 people, at least 12 are left-handed 
B: the probability that among the 100 people, more than 12 are left-handed 
C: the probability that among the 100 people, between 10 and 14 inclusive are left-handed
A)A and C
B)B and C
C)A only
D)B only

Quizplus · Accepted Answer

When using the normal approximation to the binomial distribution without a continuity correction, the probability for "more than" a certain number (in this case, more than 12 left-handed people) will be overestimated. This is because the normal distribution is continuous, and without the continuity correction, it includes part of the probability mass that should not be included for discrete outcomes. For "at least" and "between...inclusive" scenarios, the lack of continuity correction typically results in underestimation, not overestimation, of probabilities.

In a Certain Population, 11% of People Are Left-Handed