Question

68% of Americans own their home, a real estate office selects a random sample of 200 people to estimate the percentage of those people that own their home. What is the probability that at least 140 people own their home?

Answer 1

0.2709

Explanation:

Since the sample size is large enough (np > 10 and nq > 10), we can estimate this with a normal distribution.

μ = p

μ = 0.68

σ = √(pq / n)

σ = √(0.68 (1 − 0.68) / 200)

σ = 0.033

x = 140 / 200

x = 0.7

Find the z score:

z = (x − μ) / σ

z = (0.7 − 0.68) / 0.033

z = 0.61

Use a calculator or table to find the probability.

P(Z > 0.61)

1 − P(Z < 0.61)

1 − 0.7291

0.2709