Answer to Question #147798 in Statistics and Probability for David

Question

If 56% of American say they live paycheck to paycheck find the probability that five randomly selected American say they live paycheck to paycheck

Answer 1

The binomial distribution function:

$P(x=k) = nC^k(p^k)(1 – p)^{n-k} \\ n = 5 \\ k = 5 \\ P (x = 5) = 5C^5(0.56^5)(0.44^0) = 0.0551$

The probability that 5 Americans live paycheck to paycheck = 0.0551 or 5.5 %