Suppose that 19% of people in a large city used a hospital emergency room…

Question

Suppose that 19% of the people in a large city have used a hospital emergency room in the past year. If a random sample of 175 people from the city is taken, approximate the probability that at least 30 used an emergency room in the past year. Use the normal approximation to the binomial with a correction for continuity. Round answer to the nearest three decimal places, do not round any intermediate steps.

Answer 1

Binominal:

mean = n * p = 175 * 0.19

standard deviation = sqrt(n * p * (1-p)) = sqrt( 175 * 0.19 * 0.81)

x = number used an emergency room

P(x >= 30) = P(x > 29.5) applying continuity correction

compute z-score = (29.5 - mean)/standard deviation

from standard normal probability table compute P(z > z-score) = P(z < -z-score)