Question

The unemployment rate in a certain city is 8.5%. A random sample of 100 people from the labor force is drawn. Find the probability that the sample contains at least ten unemployed people.

Answer 1

Solution:

Given that,

P = 0.085

1 - P = 0.915

n = 100

Here, BIN ( n , P ) that is , BIN (100 , 0.085)

then,

n*p = 100*0.085 = 8.5 > 5

n(1- P) = 100*0.915 = 91.5 > 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 8.5

Standard deviation = =n*p*(1-p) = 100*0.085*0.915 = 7.7775

We using countinuity correction factor

P(X a ) = P(X > a - 0.5)

P(x > 9.5) = 1 - P(x < 9.5)

= 1 - P((x - ) / < (9.5 - 8.5) / 7.7775)

= 1 - P(z < 0.359)

= 1 - 0.6402   

= 0.3598

The probability that the sample contains at least ten unemployed people is 0.3598