The Republican Party wants to estimate p, the proportion of Republicans who feel Mitt Romney will be a good president. Suppose that the true proportion is p = 0.65. If a random sample of 400 individuals is selected from the population of registered Republicans, what is the approximate probability that the sample proportion, p, will be between 0.7 and 0.9? Use the continuity correction factor to obtain a more accurate result.
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Let X be the sample proportion
Then, X is approx. normally distributed with mean .65 and variance (.65)(.35)/400
P( .7<=X<=.9) = .0196
Then, X is approx. normally distributed with mean .65 and variance (.65)(.35)/400
P( .7<=X<=.9) = .0196