An investor has a 60% probability of making a $6000 profit, a 20% probability of making a $1000 profit, and a 20% probability of an $10,000 loss. What is the expected value? Should she make the investment? Assume that there is an average of p = 1.5 errors in a thousand lines of computer code. The errors occur on a random basis. What is the probability of exactly 2 errors in a specific 1000 lines of code? Which of the following involve Bernoulli trials? Pick one or more: {a} A geologist records the number of earthquakes over Richter magnitude 3.0 each year in California. (b) A quality control inspector tests electronic devices to see if they are good or defective. The probability of "good\" is 0.599. (c) A legal researcher takes a random sample of misdemeanor cases in city court, and notes whether each one goes to trial, charges are dropped, or is resolved by a plea bargain. (d) A medical researcher studying a type of cancer takes a random sample of patients, and for each patient records whether the patient survives five years. Overall the population probability of survival is p = 0.80. (Note: we solved this before as a probability problem in Module 5. This time, use the binomial approach to solve the same problem!) A married couple has 3 children. What is the probability that they have exactly 2 girls? Note: you can assume that for each birth, p(girl) = 0.5, piboy) = 0.5. A customer support telephone center gets an average of p = 3.8 calls per minute. The calls occur on a random basis. What is the probability of 3 calls in a specic minute? A recent college graduate is looking for a job. Assume that she has a probability = 0.1 of being hired each time that she interviews. She is going to keep interviewing until she gets a job offer, then stop. What is the probability that she gets her first job offer on the 6'\" interview? 10 11 A statistics instructor is much too fond of the computer game "Freecell" which is supplied with Microsoft Windows T\". On the average, she wins 30% of all her games. (You mav assume the results of the games are independent.) Out of a random sample of 30 games, what is the probability that she wins exactly 25 games? A scientist designs an instrument to detect a type of particle in cosmic radiation. On the average, 2.8 particles will strike the detector per hour. Assume that the events are random. What is the probability of 4 particles striking in a single hour? A casino has a roulette wheel. The wheel has 38 numbers that can come up when the wheel is turned. There are 18 red numbers, 18 black numbers, and two green numbers. A customer bets 51 that the next number will be red. If the number is red, the customer will receive 52 (their original dollar bet plus one extra dollar). If a black or green number comes up, the customer loses their bet and gets nothing. What is the mean or expected value? Assume that 5% of the population are allergic to peanuts. Out of a random sample of 15 people, what is the probability that one or more is allergic to peanuts? Assume that 75% of all California cars pass smog check (population proportion p = 0.75). Out of a random sample of 13 cars, what is the probability that between 14 to 16 (inclusive) pass smog check