The Honolulu Advertiser states that in Honolulu there was an average of 821 burglaries per 100,000 households in a given year. In the Kohola Drive neighborhood there are 341 homes. Let r = number of these homes that will be burglarized in a year. (a) Explain why the Poisson approximation to the binomial would be a good choice for the random variable r. B.What is n? What is p? What is λ to the nearest tenth? (Round your p to five decimal places.) C. What is the probability that there will be no burglaries this year in the Kohola Drive neighborhood? (Round your answer to four decimal places.) D. (c) What is the probability that there will be no more than one burglary in the Kohola Drive neighborhood? (Round your answer to four decimal places.) E. (d) What is the probability that there will be two or more burglaries in the Kohola Drive neighborhood? (Round your answer to four decimal places.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The Honolulu Advertiser states that in Honolulu there was an average of 821 burglaries per 100,000 households in a given year. In the Kohola Drive neighborhood there are 341 homes. Let r = number of these homes that will be burglarized in a year.
(c) What is the probability that there will be no more than one burglary in the Kohola Drive neighborhood? (Round your answer to four decimal places.)
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