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

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

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .