statistics and probability

7. [-/2 Points] DETAILS BBUNDERSTAT12 6.6.014.5. In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Do you try to pad an insurance claim to cover your deductible? About 42% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 130 insurance claims to be processed In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution in the next few days. Find the following probabilities. (Round your answers to four decimal places.) to estimate the requested probabilities. LA USE SALT What's your favorite ice cream flavor? For people who buy ice cream, the all-time favorite is still vanilla. About 29% of ice cream sales are vanilla. Chocolate accounts for only 8% of ice cream sales. Suppose that 185 customers go to a grocery store in Cheyenne, Wyoming, today to buy ice cream. [Round your answers to four decimal places.) (a) half or more of the claims have been padded LOL USE SALT (b) fewer than 45 of the claims have been padded (a) What is the probability that 50 or more will buy vanilla? (c) from 40 to 64 of the claims have been padded (b) What is the probability that 12 or more will buy chocolate? d) more than 90 of the claims have not been padded (c) A customer who buys ice cream is not limited to one container or one flavor. What is the probability that son buying ice cream will buy chocolate or vanilla? Hint: Chocolate flavor and vanilla flavor are not mutually exclusive events. Assume that the choice to buy one flavor is independent of the choice to buy another flavor. Then use the multiplication rule for Need Help? ReadIt Watch Er independent events, together with the addition rule for events that are not mutually exclusive, to compute the requested probability ('d) What is the probability that between 50 and 60 customers will buy chocolate or vanila ice cream? Hint: Use the probability of success computed in part (c). 5. [-/1.5 Points] DETAILS BBUNDERSTAT12 6.6,010.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Need Help? Read it In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 43's of strikes (while trolling) esuited in a catch. Suppose that on a given day a fleet of fishing boats got a total of 27 strikes. Find the following probabilities. (Round 8. [-/1 Points] DETAILS BBUNDERSTAT12 6.6.015.MI.S. your answers to four decimal places.) MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER LOL USE SALT Based on long experience, an airline found that about 6% of the people making reservations on a flight from Miami to Denver do not (a) 12 or fewer fish were caught show up for the flight. Suppose the airline overbooks this flight by selling 265 ticket reservations for an airplane with only 255 seats. LA USE SALT (b) 5 or more fish were caught (a) What is the probability that a person holding a reservation will show up for the flight? (c) between 5 and 12 fish were caught (b) Let n = 265 represent the number of ticket reservations. Let r represent the number of people with reservations who show up Need Help? Read It Watch It for the flight. What expression represents the probability that a seat will be available for everyone who shows up holding a reservation? OPr s 256) O P(r 2 265) O Pir = 255) 6. [-/2 Points] DETAILS BBUNDERSTAT12 6.6.011.5. O Pr s 265) MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (e) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? (Round your answer to four decimal places.) In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution o estimate the requested probabilities. It is known that 83% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store Need Help? Read It Master It chain introduces 66 new products, find the following probabilities. (Round your answers to four decimal places.) LO USE SALT a) within 2 years 47 or more fail Submit Assignment Save Assignment Progress (b) within 2 years 58 or fewer fail (c) within 2 years 15 or more succeed My Assignments (d) within 2 years fewer than 10 succeed Need Help?9. [-/1 Points] DETAILS BBUNDERSTAT12 7.3.024.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. How hard is it to reach a businessperson by phone? Let p be the proportion of calls to businesspeople for which the caller reaches the person being called on the first try. LA USE SALT (a) If you have no preliminary estimate for p, how many business phone calls should you include in a random sample to be 80% sure that the point estimate p will be within a distance of 0.03 from p? (Round your answer up to the nearest whole number.) phone calls (b) A report states that businesspeople can be reached by a single phone call approximately 17% of the time. Using this (national) estimate for p, answer part (a). (Round your answer up to the nearest whole number.) phone calls Need Help? Read It 10. [-/1 Points] DETAILS BBUNDERSTAT12 7.3.026.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year. LA USE SALT (a) If no preliminary sample is taken to estimate p, how large a sample is necessary to be 95% sure that a point estimate p will be within a distance of 0.08 from p? (Round your answer up to the nearest whole number.) small businesses (b) In a preliminary random sample of 30 small businesses, it was found that nine had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be 95% sure that a point estimate p will be within a distance of 0.080 from p? (Round your answer up to the nearest whole number.) more small businesses Need Help? Read It