Question

As of March 2018, the unemployment rate is 4.1, which means that there is a 4.1% probability that a working age adult is unemployed.

1. If we surveyed 100 adults, what is the probability that exactly 5 of them are unemployed?

2. What is the probability that no more than 2 are unemployed?

Answer 1

Mean = np = 100 * 0.041 = 4.1

Standard deviation = sqrt( np(1-p))

= sqrt( 100 * 0.041 * 0.959)

= 1.9829

a)

Using normal approximation

P( X < x) = P( Z < x - mean / SD)

With continuity correction,

P(X = 5) = P(4.5 < X < 5.5 )

= P( X < 5.5) - P( X < 4.5)

= P(Z < 5.5 - 4.1 / 1.9829) - P(Z < 4.5 - 4.1 / 1.9829)

= P( Z < 0.7060) - P( Z < 0.2017)

= 0.7599 - 0.5799

= 0.1800

b)

P( X <= 2) = P( Z <2.5 - 4.1 /1.9829)

= P(Z < -0.8069)

= 0.2099