In a city, 56 % of the population favors the incumbent, Dawn Morgan, for mayor. A simple random sample of 250 is taken. Use the normal approximation along with the continuity correction factor to find the probability that at least 133 respondents favor Dawn Morgan for mayor.
- Let be the number of respondents out of 250 that favor Dawn Morgan for mayor. Describe the distribution of and its parameters:
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( , )
- Use the random variable notation to symbolically express the probability that at least 133 respondents favor Dawn Morgan for mayor:
- Let be a normal variable that will be used to approximate the probability in question. Find the parameters of (round the answers to 2 decimal places):
( , )
- Use the random variable notation to symbolically express the approximate probability that at least 133 respondents favor Dawn Morgan for mayor:
- Use the correction for continuity:
- Find the probability (round the answer to 4 decimal places):
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