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Data from 14 cities were combined for a​ 20-year period, and the total 280 ​city-years included a total of 151 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: Homicides each​ city-year?a. 0 b. 1 c. 2 d. 3 e. 4

Respuesta :

Answer:

a) P(0)= 0.5832

b) P(1) = 0.3145

c) P(2) = 0.0848

d) P(3) = 0.0153

e) P(4) = 0.0002

Step-by-step explanation:

Number of units in the data(n) = 280

No of homocides(k) = 151

Using Poisson distribution, probability can be calculated as

P(x) = (e^-α * α^x) /x!

α = k/n

α = 151/280

α = 0.5393

a) P(0) =( e^-0.5393 * 0.5393^0) / 0!

= (0.5832 * 1) /1

= 0.5832

b) P(1) =( e^-0.5393 * 0.5393^1) / 1!

= (0.5832 * 0.5393) /1

= 0.3145

c) P(2) =( e^-0.5393 * 0.5393^2) / 2!

= (0.5832 * 0.2908) /2

= 0.1696/2

= 0.0848

d) P(3) =( e^-0.5393 * 0.5393^3) / 3!

= (0.5832 * 0.1569) /6

= 0.0915/6

= 0.0153

e) P(4) =( e^-0.5393 * 0.5393^4) / 4!

= (0.5832 * 0.0846) /24

= 0.0493/24

= 0.0002

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