Question

According to the Bureau of Labor Statistics, 7.1% of the labor force was recently unemployed. A random sample of 100 employable adults was selected.

Using the normal distribution, approximate the probability that 10 or less people from this sample are unemployed.

Using the normal distribution, approximate the probability that 6 or more people from this sample are unemployed.

Answer 1

Given

n = sample size = 100

p = 0.071

Here n*p = 7.1 > 5 and n*p*(1-p) > 6.60 > 5

So we can use normal approximation to binomial distribution.

1) we asked

P( X 10 ) = P( X < 10+0.5)

= P( X - n*p/sqrt(n*p*(1-p)) < (10.5 - 7.1)/6.60)

= P ( Z < 1.32)

Using Z table

P( X 10 ) = 0.9066

2) P( X 6 ) = P( X > 6-0.5)

=P( X-n*p/sqrt(n*p*(1-p)) >( 5.5 - 7.1)/6.60))

= P ( Z > -0.62)

= 1 - P( Z <-0.62)

= 1- 0.2676

P ( X 6 ) = 0.7324