PSTAT W120A, Summer 2016 Assignment 2.A Due Wednesday Aug. 10 Directions: Please write up your solutions and submit them on GauchoSpace by the end of the day on Wednesday. We prefer the submission to be single pdf file if possible. Bonus points will be awarded for organization and neatness. Lesson 5 Binomial Experiments 1. A complicated mechanical system contains 8 components. If there is a 18% chance that each component will fail during processing, and components fail independently of each other, then (a) What is the probability that fewer than 3 components will fail? (b) What is the most likely number of failures? 2. There are 16,408 students on campus at UCSB and 385 of them are statistics majors. Suppose that we choose 10 students randomly from the campus so that each choice was independent of the others and every student was equally likely to be chosen. (a) What is the probability that the first student chosen is a statistics major? (b) What is the probability that exactly one of those ten students is a Statistics major? Lesson 6 Normal Approximation to the Binomial 3. Once again, we have 16,408 undergraduate students on campus of which there are 385 stats majors. This time we collect 800 students independently and equally likely. (a) How many statistics majors on average would we expect in our sample? (b) Using the normal approximation, what is the probability that we would have more than 10 statistics majors in those 800 students? 4. We flip a fair coin 3000 times. (a) What is the probability that we get more than 1550 heads? (b) What is the probability that fewer than 49% of the flips come up heads? (c) What is the probability of between 1497 and 1505 heads? You may need to use an appropriate approximation to do the calculation. Use the online Normal CDF Calculator to get the normal probabilities. 1 of 1