Question

Suppose that 45 % of the population of U.S. voters favors a particular presidential candidate. If a random sample of 75 voters is chosen, approximate the probability that more than 35 favor this candidate. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.) Problem Page Suppose that 45 % of the population of U.S. voters favors a particular presidential candidate. If a random sample of 75 voters is chosen, approximate the probability that more than 35 favor this candidate. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.)

Answer 1

n=	75	p=	0.4500
here mean of distribution=μ=np=		33.75
and standard deviation σ=sqrt(np(1-p))=		4.3084
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

probability that more than 35 favor this candidate:

probability =

P(X>35.5)

=

P(Z>0.406)=

1-P(Z<0.41)=

1-0.6591=

0.341

( please try 0.342 if ti-84 calculator is to be used instead of table)