Transportation officials tell us that 80% of drivers wear seat belts while driving. What is the probability that between 538 and 546 drivers in a sample of 700 drivers wear seat belts?
+33665 If the probability of a single driver wearing a seatbelt is 0.8, then the probability of k out of 700 drivers wearing their seat belts is:
$$0.8^k0.2^{700-k}nCr(700,k)$$
where the last term is the number of ways of choosing groups of size k from 700. To answer the question here we need to sum this from k = 538 to k=546:
$$\sum_{k=538}^{546}0.8^k0.2^{700-k}nCr(700.k) = 0.084$$
.
+33665 If the probability of a single driver wearing a seatbelt is 0.8, then the probability of k out of 700 drivers wearing their seat belts is:
$$0.8^k0.2^{700-k}nCr(700,k)$$
where the last term is the number of ways of choosing groups of size k from 700. To answer the question here we need to sum this from k = 538 to k=546:
$$\sum_{k=538}^{546}0.8^k0.2^{700-k}nCr(700.k) = 0.084$$
.
