Question

eBook Exercise 5.29 (Algorithmic)) In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005) a. In a sample of 6 workers, what is the probability that exactly three workers take public transportation daily (to 4 decimals including interim calculations)? b. In a sample of 6 workers, what is the probability that at least three workers take public transportation dally (to 4 decimals including interim calculations)?

Answer 1

X follow binomial distribution with n = 6 , p =0.3

${\displaystyle f(k,n,p)=\Pr(k;n,p)=\Pr(X=k)={\binom {n}{k}}p^{k}(1-p)^{n-k}}$

a)

P(X = 3) = 0.1852

b)

P(X >= 3) = 0.2557