Answer:
Feature 1- Statement A, Feature 2-Statement 2, Feature 3- Statement 1
Let X be the number of burglaries in a week. X follows Poisson distribution with mean of 1.9
We have to find the probability that in a randomly selected week the number of burglaries is at least three.
P(X ≥ 3 ) = P(X =3) + P(X=4) + P(X=5) + ........
= 1 - P(X < 3)
= 1 - [ P(X=2) + P(X=1) + P(X=0)]
The Poisson probability at X=k is given by
P(X=k) = ![\frac{e^{-mean} mean^{x}}{x!}](https://tex.z-dn.net/?f=%20%5Cfrac%7Be%5E%7B-mean%7D%20mean%5E%7Bx%7D%7D%7Bx%21%7D%20%20%20%20)
Using this formula probability of X=2,1,0 with mean = 1.9 is
P(X=2) = ![\frac{e^{-1.9} 1.9^{2}}{2!}](https://tex.z-dn.net/?f=%20%5Cfrac%7Be%5E%7B-1.9%7D%201.9%5E%7B2%7D%7D%7B2%21%7D%20%20%20%20)
P(X=2) = ![\frac{0.1495 * 3.61}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B0.1495%20%2A%203.61%7D%7B2%7D%20%20)
P(X=2) = 0.2698
P(X=1) = ![\frac{e^{-1.9} 1.9^{1}}{1!}](https://tex.z-dn.net/?f=%20%5Cfrac%7Be%5E%7B-1.9%7D%201.9%5E%7B1%7D%7D%7B1%21%7D%20%20%20%20)
P(X=1) = ![\frac{0.1495 * 1.9}{1}](https://tex.z-dn.net/?f=%20%5Cfrac%7B0.1495%20%2A%201.9%7D%7B1%7D%20%20)
P(X=1) = 0.2841
P(X=0) = ![\frac{e^{-1.9} 1.9^{0}}{0!}](https://tex.z-dn.net/?f=%20%5Cfrac%7Be%5E%7B-1.9%7D%201.9%5E%7B0%7D%7D%7B0%21%7D%20%20%20%20)
P(X=0) = ![\frac{0.1495 * 1}{1}](https://tex.z-dn.net/?f=%20%5Cfrac%7B0.1495%20%2A%201%7D%7B1%7D%20%20)
P(X=0) = 0.1495
The probability that at least three will become
P(X ≥ 3 ) = 1 - [ P(X=2) + P(X=1) + P(X=0)]
= 1 - [0.2698 + 0.2841 + 0.1495]
= 1 - 0.7034
P(X ≥ 3 ) = 0.2966
The probability that in a randomly selected week the number of burglaries is at least three is 0.2966
Answer:
-2
Step-by-step explanation:
If we have an equation of the form y = mx +b then the y-intercept is b.
So now here we have y =-x - 2. Therefore b = -2 and we conclude the y-intercept is -2.
Answer:
4. F
5.C
6.G
7.D
8.A
9.E
10.B
Step-by-step explanation:
Step-by-step explanation:
4. The Trane air conditioner cooled off 1000 cubic feet in 10 minutes. How long would it take the same unit to cool off 3000 cubic feet?