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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) =
Using this formula probability of X=2,1,0 with mean = 1.9 is
P(X=2) =
P(X=2) =
P(X=2) = 0.2698
P(X=1) =
P(X=1) =
P(X=1) = 0.2841
P(X=0) =
P(X=0) =
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:
The equation of the tangent line passing through the point (-2,3) is
4 x + y +5 =0
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given that the slope of the tangent</em>
<em> </em><em></em>
<em> m = -2( 3-1) = -4</em>
<em>Given point x = -2</em>
<em> y = f(-2) =3</em>
<em>∴The given point ( x₁ , y₁) = ( -2 ,3)</em>
<u><em>Step(ii):-</em></u>
The equation of the tangent line passing through the point (-2,3)
y -3 = -4( x+2)
y-3 = -4x -8
4x + y -3+8=0
4x +y +5=0
<u><em>Step(iii):-</em></u>
<em>The equation of the tangent line passing through the point (-2,3) is</em>
<em> 4 x + y +5 =0</em>
<em></em>