Answer: Aircraft Accidents. In Exercises 58, assume that the Poisson distribution

Notation In analyzing hits by V1 buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km 2 . A total of 535 bombs hit the combined area of 576 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In applying Formula 59, identify the values of , x, and e. Also, briefly describe what each of those symbols represents.

Tornadoes During a recent 46year period, New York State had a total of 194 tornadoes that measured 1 or greater on the Fujita scale. Let the random variable x represent the number of such tornadoes to hit New York State in one year, and assume that it has a Poisson distribution. What is the mean number of such New York tornadoes in one year? What is the standard deviation? What is the variance?

Poission Approximation to Binomial Assume that we want to find the probability of getting at least one win when playing the Texas Pick 3 lottery 50 times. For one bet, there is a 1/1000 probability of winning. If we want to use the Poisson distribution as an approximation to the binomial, are the requirements satisfied? Why or why not?

Poisson Approximation to Binomial Assume that we plan to play the Texas Pick 3 lottery 100 times. For one bet, there is a 1/1000 probability of winning. If we want to use the Poisson distribution as an approximation to the binomial, are the requirements satisfied? If we use the Poisson distribution to find the probability of 101 wins, we get an extremely small positive number, so is it correct to conclude that the probability of 101 wins is possible, but highly unlikely?

Aircraft Accidents. In Exercises 58, assume that the Poisson distribution applies, assume that the mean number of aircraft accidents in the United States is 8.5 per month (based on data from the National Transportation and Safety Board), and proceed to find the indicated probability Find P(0), the probability that in a month, there will be no aircraft accidents. Is it unlikely to have a month with no aircraft accidents?

Aircraft Accidents. In Exercises 58, assume that the Poisson distribution applies, assume that the mean number of aircraft accidents in the United States is 8.5 per month (based on data from the National Transportation and Safety Board), and proceed to find the indicated probability Find P(6), the probability that in a month, there will be 6 aircraft accidents. Is it unlikely to have a month with exactly 6 aircraft accidents?

Aircraft Accidents. In Exercises 58, assume that the Poisson distribution applies, assume that the mean number of aircraft accidents in the United States is 8.5 per month (based on data from the National Transportation and Safety Board), and proceed to find the indicated probabilityFind P(10), the probability that in a month, there will be 10 aircraft accidents. Is it unlikely to have a month with exactly 10 aircraft accidents?

Aircraft Accidents. In Exercises 58, assume that the Poisson distribution applies, assume that the mean number of aircraft accidents in the United States is 8.5 per month (based on data from the National Transportation and Safety Board), and proceed to find the indicated probability Find P(12), the probability that in a month, there will be 12 aircraft accidents. Is it unlikely to have a month with exactly 12 aircraft accidents?

In Exercises 916, use the Poisson distribution to find the indicated probabilities. Earthquakes in the United States Various sources provide different earthquake data, but assume that for a recent 41year period in the United States, there were 268 earthquakes measured at 6.0 or higher on the Richter scale (based on U.S. Geological Survey data). a. Find the mean number of earthquakes per year. b. Find the probability that in a given year, there is at least one earthquake in the United States that measures 6.0 or higher on the Richter scale. c. Is it unlikely to have a year without any earthquakes that measure 6.0 or higher on the Richter scale? Why or why not?

In Exercises 916, use the Poisson distribution to find the indicated probabilities.Earthquakes in the World Various sources provide different earthquake data, but assume that for a recent 41year period in the world, there were 5469 earthquakes measured at 6.0 or higher on the Richter scale (based on U.S. Geological Survey data). a. Find the mean number of earthquakes per year. b. Find the probability that in a given year, there are exactly 133 earthquakes that measures 6.0 or higher on the Richter scale. c. If, in a particular year, there are exactly 133 earthquakes that measure 6.0 or higher on the Richter scale, would it make sense to report that this is a year with an unusual number of earthquakes? Why or why not?

In Exercises 916, use the Poisson distribution to find the indicated probabilities.Radioactive Decay Radioactive atoms are unstable because they have too much energy. When they release their extra energy, they are said to decay. When studying cesium137, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 977,287 radioactive atoms, so 22,713 atoms decayed during 365 days. a. Find the mean number of radioactive atoms that decayed in a day. b. Find the probability that on a given day, 50 radioactive atoms decayed.

In Exercises 916, use the Poisson distribution to find the indicated probabilities.Deaths from Horse Kicks A classical example of the Poisson distribution involves the number of deaths caused by horse kicks to men in the Prussian Army between 1875 and 1894. Data for 14 corps were combined for the 20year period, and the 280 corpsyears included a total of 196 deaths. After finding the mean number of deaths per corpsyear, find the probability that a randomly selected corpsyear has the following numbers of deaths: (a) 0, (b) 1, (c) 2, (d) 3, (e) 4. continued The actual results consisted of these frequencies: 0 deaths (in 144 corpsyears) 1 death (in 91 corpsyears) 2 deaths (in 32 corpsyears) 3 deaths (in 11 corpsyears) 4 deaths (in 2 corpsyears). Compare the actual results to those expected by using the Poisson probabilities. Does the Poisson distribution serve as a good tool for predicting the actual results?

In Exercises 916, use the Poisson distribution to find the indicated probabilities.. World War II Bombs In Exercise 1 we noted that in analyzing hits by V1 buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km 2 . A total of 535 bombs hit the combined area of 576 regions. a. Find the probability that a randomly selected region had exactly 2 hits. b. Among the 576 regions, find the expected number of regions with exactly 2 hits. c. How does the result from part (b) compare to this actual result: There were 93 regions that had exactly 2 hits?

In Exercises 916, use the Poisson distribution to find the indicated probabilities.Disease Cluster Neuroblastoma, a rare form of malignant tumor, occurs in 11 children in a million, so its probability is 0.000011. Four cases of neuroblastoma occurred in Oak Park, Illinois, which had 12,429 children. a. Assuming that neuroblastoma occurs as usual, find the mean number of cases in groups of 12,429 children. b. Using the unrounded mean from part (a), find the probability that the number of neuroblastoma cases in a group of 12,429 children is 0 or 1. c. What is the probability of more than one case of neuroblastoma? d. Does the cluster of four cases appear to be attributable to random chance? Why or why not?

In Exercises 916, use the Poisson distribution to find the indicated probabilities. Chocolate Chip Cookies In the production of chocolate chip cookies, we can consider each cookie to be the specified interval unit required for a Poisson distribution, and we can consider the variable x to be the number of chocolate chips in a cookie. Table 31 is included with the Chapter Problem for Chapter 3, and it includes the numbers of chocolate chips in 34 different Keebler cookies. The Poisson distribution requires a value for , so use 30.4, which is the mean number of chocolate chips in the 34 Keebler cookies. Assume that the Poisson distribution applies. a. Find the probability that a cookie will have 26 chocolate chips, then find the expected number of cookies with 26 chocolate chips among 34 different Keebler cookies, then compare the result to the actual number of Keebler cookies with 26 chocolate chips. b. Find the probability that a cookie will have 30 chocolate chips, then find the expected number of cookies with 30 chocolate chips among 34 different Keebler cookies, then compare the result to the actual number of Keebler cookies with 30 chocolate chips

In Exercises 916, use the Poisson distribution to find the indicated probabilities.Chocolate Chip Cookies Consider an individual chocolate chip cookie to be the specified interval unit required for a Poisson distribution, and consider the variable x to be the number of chocolate chips in a cookie. Table 31 is included with the Chapter Problem for Chapter 3, and it includes the numbers of chocolate chips in 40 different reduced fat Chips Ahoy cookies. The Poisson distribution requires a value for , so use 19.6, which is the mean number of chocolate chips in the 40 reduced fat Chips Ahoy cookies. Assume that the Poisson distribution applies. a. Find the probability that a cookie will have 18 chocolate chips, then find the expected number of cookies with 18 chocolate chips among 40 different reduced fat Chips Ahoy cookies,

Poisson Approximation to Binomial Distribution An experiment consists of rolling a single die 12 times and the variable x is the number of times that the outcome is 6. a. Can the Poisson distribution be used to find the probability that the outcome of 6 occurs exactly 3 times? Why or why not? b. If the Poisson distribution is used, is the result OK? Why or why not?