In a certain city of several million people, 6.9% of the adults are unemployed. If a random sample of 270 adults in this city is selected

Question

In a certain city of several million people, 6.9%

of the adults are unemployed. If a random sample of 270

adults in this city is selected, approximate the probability that more than 15

in the sample are unemployed. 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.

Answer 1

proportion unemployed (p) = 6.9% = 0.069

mean = sample size (n) * p = 270 * 0.069 = 18.63

standard deviation = sqrt (n * p * (1-p)) = sqrt(270*0.069*0.931) = 4.19

x = number of adults

z-stat = (x - mean)/standard deviation) = (15-18.63)/4.19 = -0.866

P(x > 15) = P(z > -0.866) = 1 - P(z < -0.866) = 1 - 0.1929 = 0.08071