In San Francisco 30 of workers take public transportation da

In San Francisco, 30% of workers take public transportation daily (USA Today, December 21,2005). In a sample of 7 workers, what is the probability that exactly three workers take public transportation daily (to 4 decimals)? In a sample of 7 workers, what is the probability that at least three workers take public transportation daily (to 4 decimals)?

Solution

it\'s a Binomial Distribution problem. First, the outcomes can be classified as success(workers take public transportation) and failure(workers do not take public transportation). Next, we are given that Pr(success) = .3 while Pr(failure) = .7 1) We have 10 trials. Thus, Pr(exactly 3 workers take public transportation daily) = 10C3 * .3^3 * .7^7 = 120 * .027 * .0823543 = .2668 2) Again, we have 10 trials. Pr(at least 3 workers take public transportation daily) = 1 - Pr(less than 3 workers take public transportation daily) (*They are complements*) = 1 - Pr(2 take) - Pr(1 takes) - Pr(0 take) = 1 - .2335 -.1211 - .0282 = .6172.