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Normal Approximation in the Binomial Distribution

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The next North Carolina gubernatorial election will be held in 2016. Suppose that 52% of North Carolina voters actually support Candidate A in that election.

a) What is the probability that a poll of a simple random sample of 100 NC voters will result in at least half of those polled favoring the other candidate? Use the normal approximation (no continuity correction) and give your answer to four decimal places.
P(X≥ 50) =

b) What is the probability that a poll of a simple random sample of 700 NC voters will result in at least half of those polled favoring the other candidate? Use the normal approximation (no continuity correction) and give your answer to four decimal places.
P(X ≥ 350) =

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a)
This question is actually a binomial distribution question, but the problem says to use the normal distribution to approximate the answer. Since the question refers to "favoring the other candidate", the probability of success is 100% - 52%.
n = 100
p = .48 ...

Solution provided by:
J Pye, MSc
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  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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