Question

Five percent of workers in a certain city use public transportation to get work. If you randomly select 250 workers and ask them if they use public transportation to get to work, find the probability that more than 16 workers will say yes.

Answer 1

ANSWER;

n = 250 p = 0.05 For this case, applying normal approximation to binomial, we get: mean = n*p= 12.5 variance = n*p*(1-p) = 11.875 std dev = 3.446

We want to Find : P(X = 15) = P( 15.5 < X < 16.5) ( continuity correction) We convert to standard normal form, Z ~ N(0,1) by z1 = (x1 - u )/s so z1 = (15.5 - 12.5 )/3.446 = 0.87 so z2 = (16.5 - 12.5 )/3.446 = 1.16 P( 15.5 < X < 16.5) = P(z1 < Z < z2) = P( Z < 1.16) - P(Z < 0.87) = 0.877 - 0.8078 = 0.0692 _ _ _ _ _ _ _ _ _ (From Z-table)