Use the Normal model to approximate the Binomial.
-According to the Census Bureau, 68% of Americans owned their own home in 2003.
A local real estate office wants to see if this is the case for its area. The office selects a
Random sample of 200 people to estimate the percentage who own their own homes.
What is the probability that at least 140 people own their own home?
A) 0.7291
B) 0.2709
C) 0.4598
D) 0.5402
E) 0.1299

Question

Quizplus · Accepted Answer

To approximate the Binomial distribution with a Normal distribution, we use the mean np = 200 * 0.68 = 136 and standard deviation sqrt(np(1-p)) = sqrt(200 * 0.68 * 0.32) ≈ 6.53. We find the z-score for 139.5 (continuity correction) and calculate the probability of z being greater than this value, which is approximately 0.2709.

Use the Normal Model to Approximate the Binomial