Question

I need help understanding what a continuity correction is, and when to add it to a normal distribution probability. Here is a problem from my lecture that this question corresponds to:

A nationwide random sample of 2500 adults were asked if they agreed or disagreed with the statement “I like buying clothes, but shopping is often frustrating and time-consuming.” Suppose that in fact 60% of the population of all adult U.S. residents would say “agree” if asked this question. What is the probability that 1520 or more of the sample agree? Assume each person is asked independently of others surveyed.

The final answer is 0.2119 or 21.19% probability of observing 1520 or more of the sample who agree. But I do not know how this answer was calculated. Please walk me through the steps to arrive at this answer.

Answer 1

Population proportion, p = 0.60

Sample size, n= 2500

Mean,

Standard deviation,

Probability that 1520 or more of the sample agree, P( X>=1520) =

Using continuity correction:

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