10. There are two conditions that you have to check before using the normal approximation when X is binomial. a. Write down the two conditions. b. Why do we have to check BOTH conditions rather than just one, to be able to use the normal approximation? (Including an example with your explanation is OK.) 11. Suppose you ip a fair coin 7 times, and let X be the total number of tails. What is the probability that X is greater than 1? (Hint, what is p when you ip a fair coin?) 12. Suppose it is reported that 10% of OSU business students major in international marketing. You sample 200 OSU business students at random. Let X = the number of students in the sample who major in international marketing. a. b. How many students in your sample do you EXPECT to major in int'l marketing, according to the above information? What is the probability that your sample finds that at least 15 students major in international marketing? Are your findings from part (b) typical of what you EXPECTED to get in part (a)? Why or why not? 13. Suppose X is binomial with p = .90. What does n have to be (at a minimum) to use the normal approximation for X? 14. 15. 16. 17. Suppose X is binomial with p = .10. What does n have to be (at a minimum) to use the normal approximation for X? Explain why the same n works for both of the previous problems. Suppose 20% of a bank's customers report being unsatisfied. You take a sample of 20 customers at random and count the number of unsatisfied customers. a. b. c. Is the distribution of the number of unsatisfied customers from this sample binomial? Justify. What is the probability that 5 customers are unsatisfied? USING THE FORMULA AND THE TABLE TO VERIFY: What is the probability that at most 2 customers are unsatisfied? Show your work. Suppose a media report claims that 25% of children are addicted to video games. You think the percentage is higher than that. You take a random sample of 200 children and find that at least 70 of them are addicted to video games. a. b. What is the chance of this result happening? Based on your results do you believe the claim that 25% of children are addicted to video games? Why or why not? 18. Suppose we have a 20 question MCTF test where each question has 4 possible answers. a. If you guess on all the questions, and you let X be the number you get right, what is the mnnn of V") 'ATLYY Ann I-L:r\\ niiml'nm 1+".er nnnnn")