Suppose that 17% of the people in a large city have used a hospital emergency room in the past year. If a random sample of

Question

Suppose that 17%

of the people in a large city have used a hospital emergency room in the past year. If a random sample of 120

people from the city is taken, approximate the probability that more than 19

used an emergency room in the past year. 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

x is number of people. x is binomially distributed with p = 0.17, n = 120

For binomial distribution mean = np = 20.4, standard deviation = sqrt(n*p*(1-p)) = 4.11

z statistic = (x - mean)/standard deviation. is N(0,1)

P(x > 19) = P(z > (19 - 20.4)/4.11) = P(z > -0.34) = 1 - P(z < -0.34) = 1 - 0.3669 = 0.6331