07 Jan Alex will conclude that the

MATH225 Statistical Reasoning for the Health Sciences

Week 4 Assignment Distribution with Probability Rules

Question A roulette wheel has 38 slots, numbered 1 to 36, with two additional green slots labeled 0 and 00. Jim, a dealer at a roulette table, tests the roulette wheel by spinning a ball around the wheel repeatedly and seeing where the ball lands. The ball has an equally likely chance of landing in each slot. If Jim spins the ball around the wheel 25 times, what is the probability that the ball lands in a green slot at most twice? Use Excel to find the probability.

Question A database system assigns a 32-character ID to each record, where each character is either a number from 0 to 9 or a letter from A to F. Assume that each number or letter being selected is equally likely. Find the probability that at least 20 characters in the ID are numbers. Use Excel to find the probability.

Question Kevin works for a company that manufactures solar panels. In a large batch of solar panels, about 1 in 200 is defective. Suppose that Kevin selects a random sample of six solar panels from this batch. What is the probability that none of the solar panels are defective? Use Excel to find the probability.

• Round your answer to three decimal places.

Question Alex wants to test the reliability of “lie detector tests,” or polygraph tests. He performs a polygraph test on a random sample of 12 individuals. If there is more than a 50% chance that the tests result in no false positives (that is, the test does not result in a true statement being recorded as a lie), Alex will conclude that the tests are reliable. If the probability of a lie detector test resulting in a false positive is 5.5%, what will Alex conclude? Use Excel to find the probability, rounding to three decimal places.

Alex will conclude that the test is reliable since the probability of no false positives is less than 0.5.

Alex will conclude that the test is not reliable since the probability of no false positives is greater than 0.5.

Alex will conclude that the test is not reliable since the probability of no false positives is less than 0.5.

Alex will conclude that the test is reliable since the probability of no false positives is greater than 0.5.

Question A computer graphics card manufacturer is testing an improvement to its production process. If a sample of 100 graphics cards manufactured using the new process has a less than 10% chance of having 3 or more defective graphics cards, then the manufacturer will switch to the new process. Otherwise, the manufacturer will stay with its existing process. If the probability of a defective graphics card using the new process is 0.9%, will the manufacturer switch to the new production process?

Yes, because the probability of having 3 or more defective graphics cards is greater than 0.10.

Yes, because the probability of having 3 or more defective graphics cards is less than 0.10.

No, because the probability of having 3 or more defective graphics cards is less than 0.10.

No, because the probability of having 3 or more defective graphics cards is greater than 0.10.

Question Kelsey, a basketball player, hits 3-point shots on 38.1% of her attempts. If she takes 14 attempts at 3-point shots in a game, what is the probability that she hits exactly six of them? Use Excel to find the probability.