unemployed probability

Question

If 7 percent of the workers in an area are unemployed , what is the probability that in a sample of 150 workers more than 15 will be unemployed ? ( USE NAB ).Explain why you have applied Normal approximation to Binomial.

Answer 1

n = 150

phat = (15/150) = .10

p = .07

Standardize the normal random variable

z = (phat - p) / √ [p(1-p) / n]

z = (.10 - .07) / √ [.07(1-.07) / 150]

z = .03 / √.000434

z = 1.44

The question asks what is the probability that more than 15 workers will be unemployed. So, it's asking for the area to the right of a z-score of 1.44. Look up probability using a z-score of 1.44, and subtract from one.

The probability is .9251

1 - .9251 = .0749 or 7.49%

We apply normal distribution to a binomial due to the Central Limit Theorem. The Central Limit Theorem states that if a population is distributed binomial, the distribution of the sample proportion is binomial. If the population is distributed binomial and n > 30, the distribution will be normal.