A multiple-choice examination consists of 65 questions, each having possible choices a, b, c, d, and e. Approximate the probability that a student will get more than 11 answers correct if she randomly guesses at each answer. (Note that, if she randomly guesses at each answer, then the probability that she gets any one answer correct is o.2.) Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.)

Suppose that a company gains an average of 7 customers per $700 spent on advertising. If the company spends $700 on advertising, find the probability of gaining at least 13 customers. Part 1 out of 2Find the mean number λ. Round to the nearest tenth.  λ = _______

Can you tell the difference?  Is this a Binomial or Hypergeometric Model? 1. At a certain manufacturing company, approximately 5% of the products are defective. We are interested in calculating the probability that the third defective is the 20th one sampled. 2. An assembly line produces products that they put into boxes of 50. The inspector then randomly picks 3 items inside a box to test to see if they are defective. In a box containing 4 defectives, they are interested in the probability that at least one of the three items sampled is defective.  3. In a capture-recapture experiment, 20 animals were captured, tagged and released. A few weeks later, a sample of 40 of these animals is capture and we are interested in the number of animals in our sample that are tagged. 4. A husband has 7 tasks on his to-do list and a wife has 10 things on her to-do list. Five tasks are randomly picked out of these 17 tasks. We are interest in the expected number of tasks the wife will have to do. 5. A…

K Suppose a basketball player is an excellent free throw shooter and makes 92% of his free throws (i.e., he has a 92% chance of making a single free throw). Assume that free throw shots are independent of one another. Suppose this player gets to shoot three free throws. Find the probability that he misses all three consecutive free throws. Round to four decimal places. OA. 0.2213 OB. 0.9995 OC. 0.0005 OD. 0.7787