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:
84.1379%
Step-by-step explanation:
122 / 145 = 0.841379
(0.841379)(100) = 84.1379%
The quadratic function is given by the equation ![h(t)=-0.075t^2+0.6t+2.5.](https://tex.z-dn.net/?f=h%28t%29%3D-0.075t%5E2%2B0.6t%2B2.5.)
The maximal height will be at vertex. Find t-coordinate of the parabola vertex:
![t_{vertex}=-\dfrac{b}{2a}=-\dfrac{0.6}{2\cdot (-0.075)}=4\text{ seconds.}](https://tex.z-dn.net/?f=t_%7Bvertex%7D%3D-%5Cdfrac%7Bb%7D%7B2a%7D%3D-%5Cdfrac%7B0.6%7D%7B2%5Ccdot%20%28-0.075%29%7D%3D4%5Ctext%7B%20seconds.%7D)
At t=4,
![h(4)=-0.075\cdot 4^2+0.6\cdot 4+2.5=-1.2+2.4+2.5=3.7\text { feet. }](https://tex.z-dn.net/?f=h%284%29%3D-0.075%5Ccdot%204%5E2%2B0.6%5Ccdot%204%2B2.5%3D-1.2%2B2.4%2B2.5%3D3.7%5Ctext%20%7B%20feet.%20%7D)
Answer: it will take 4 seconds for the ball to reach the maximal height of 3.7 feet.
Answer: My answer was wrong sorry
Step-by-step explanation:
Answer:
3 - 151 x
Step-by-step explanation:
d/dx(5×3 x - 10×15 x - 3 x - 10 x - (3 x - 3)) = -151
Indefinite integral:
integral(3 - 151 x) dx = 3 x - 75.5 x^2 + constant
Definite integral after subtraction of diverging parts:
integral_0^∞ ((3 - 151 x) - (3 - 151 x)) dx = 0