Use the Normal model to approximate the Binomial.
-The unemployment rate of persons with a disability is typically higher than for those
With no disability. Recent statistics report that this rate is 14.5%. An advocacy group in
A large city located in the southeastern region of the U.S. selected a random sample of
250 persons with a disability. What is the probability that at least 20 persons in this
Sample are unemployed?
A) 0.8686
B) 0.9982
C) 0.6573
D) 0.1314
E) 0.0018

Question

Quizplus · Accepted Answer

To approximate the Binomial distribution with a Normal distribution, we use the mean (np) and standard deviation (sqrt(np(1-p))) of the Binomial distribution. Here, n = 250 and p = 0.145. The mean is 250*0.145 = 36.25 and the standard deviation is sqrt(250*0.145*0.855) ≈ 5.47. We find the z-score for 19.5 (continuity correction for "at least 20") and use the standard normal distribution to find the probability. The probability that at least 20 persons are unemployed is approximately 0.9982.

Use the Normal Model to Approximate the Binomial