Please show all work!!! Thanks! Data from 14 cities were combined for a 20-year

Question

Please show all work!!! Thanks!

Data from 14 cities were combined for a 20-year period, and the total 280 city-years included a total of 92 homicides. After finding the mean number of homicides per city-year, find the probability that a randomly selected city-year has the following numbers of homicides, then compare the actual results to those expected by using the Poisson probabilities e. 4 Homicides each city-year Actual results d. 3 201 67 a. P(0) (Round to four decimal places as needed.) (Round to four decimal places as needed.) c. P(2) (Round to four decimal places as needed.) d. P(3) (Round to four decimal places as needed.) e. P(4) (Round to four decimal places as needed.) The actual results consisted of 201 city-years with 0 homicides, 67 city-years with one homicide; 11 city-years with two homicides, 1 city-year with three homicides, 0 city-years with four homicides 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? O O No, the results from the Poisson distribution probabilities do not match the actual results Yes, the results from the Poisson distribution probabilities closely match the actual results

Explanation / Answer

Solution:-
a. P(0) = 201/(201+67+11+1+0)
= 201/280
= 0.7179

b. P(1) = 67/(201+67+11+1+0)
= 67/280
= 0.2393

c. P(2) = 11/280 = 0.0393

d. P(3) = 1/280 = 0.0036

e. P(0) = 0

=> option A.

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