8. If 1.2% of the population has a certain disease, compute the probability that exactly three of two hundred randomly chosen individuals will have the disease. Carry out this computation to four decimal places using (a) the binomial distribution and (b) the Poisson distribution.
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- In a recent year, a hospital had 4142 births. Find the mean number of births per day, then use that result and the Poisson distribution to find the probability that in a day, there are 13 births. Does it appear likely that on any given day, there will be exactly 13 births?A bakery produces an average of 50 loaves of bread per day. The number of loaves produced by the bakery follows a Poisson distribution. What is the probability that the bakery will sell at least two loaves of bread in a day? Explain each step along with the computation.8. Final: For recent period of 100 years, there were 530 Atlantic hurricanes. Assume the Poisson distribution is a suitable model, find the probability that less than 3 hurricanes in a randomly selected year. O a. .1901 O b. None of the above O C. .2075 O d. .3701 O e..1016 日 田
- The number of typing errors made by a typist has a Poisson distribution with an average of three and a half errors per page. If five or more errors appear on a given page, the typist must retype the whole page. What is the probability that the typist makes 3 errors on a page? What is the probability that a randomly selected page does not need to be retyped?A sample of a radioactive material is studied in a lab. There are 741 gamma ray emissions over 130 seconds. Use the Poisson distribution to find the probability that 1 or fewer gamma rays are emitted in a given second. Do not round intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.) ?Consider a Poisson distribution with an average of 4 customers per minute at the local grocery store. If X = the number of arrivals per minute:Find the probability of 8 customers or less arriving within a minute. Find the probability of more than 7 customers arriving within a minute. Find the probability of 3 customers arriving within a minute.
- 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 20-year period, and the 280 corps-years included a total of 196 deaths. After finding the mean number of deaths per corps-year, find the probability that a randomly selected corps-year has the following numbers of deaths: (a) 0, (b)1, (c)2, (d)3, (e)4. The actual results consisted of these frequencies: 0 deaths (in 144 corps-years) ;1 death (in 91 corps-years); 2 deaths (in 32 corps-years); 3 deaths (in 11 corps-years); 4 deaths (in 2 corps-years). 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?A certain kind of sheet metal has, on average, 4 defects per 20 square feet.Assuming a Poisson distribution, find the probability that a 28 square foot metal sheet has at least 7 defects. Round your answer to three decimal places.