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 only
C) B and C
D) A 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 only
C) B and C
D) A only

Quizplus · Accepted Answer

When using the normal approximation without continuity correction, the probability for "more than 12" (B) will be too large because the approximation does not account for the discrete nature of the binomial distribution.

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