Question

According to the Bureau of Labor Statistics, the unemployment rate in Detroit in June 2014 was 11 approximately 10%. If a random sample of 15 people living in Detroit at that time was taken, find the probability that two or fewer were unemployed.

Answer 1

Let X = Number of unemployed people in Detroit.

p = probability of unemployment = 0.10

X follows Binomial distribution with parameter n = 15 and p = 0.10

The pmf of Binomial distribution is,

We want probability that,

Now first we obtain probability at X = 0,1,2

  

Similarly ,

P(X =1) = 0.3432

P(X =2) = 0.2669

Hence