Random Variables?

If 65 percent of the population of a large community is in favor of a proposed rise in school taxes, approximate the probability that a random sample of 100 people will contain





(a) at least 50 who are in favor of the proposition


(b) between 60 and 70 inclusive who are in favor;


(c) fewer than 75 in favor.

Random Variables?
I think they want you to use the normal approximation, perhaps with continuity correction, to the given binomial distribution (which has mean np = 100 * 0.65 = 65 and variance np(1-p) = 100 * 0.65 * (1 - 0.65) = 42.25, standard deviation = sqrt(variance) = 6.5).





It is also easy enough with a computer to compute the exact probabilities.





Dan

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