The monthly worldwide average number of air- plane crashes of commercial airlines is 3.5. What is the probability that there will be (a) at least 2 such accidents in the next month?
(b) at most 1 accident in the next month?

The probability that there will be

(a) at least 2 such accidents in the next month?

= 0.864

(b) at most 1 accident in the next month?

= 0.136

Step-by-step explanation:

This is a Poisson Distribution question.

The formula is given as:

For X = x ,

= λ^x × e^-λ/x!

The monthly worldwide average number of air- plane crashes of commercial airlines is 3.5. What is the probability that there will be

(a) at least 2 such accidents in the next month?

= λ^x × e^-λ/x!

λ = 3.5

x = at least 2 such accidents

x ≥ 2

= 1 - [P(x = 0) + P(x = 1)]

= 1 - [(3.5^0 × e^-3.5/0!)+ (3.5^1 × e^-3.5/1!)]

= 1 - [ 1 × 0.0301973834 + 3.5 × 0.0301973834]

1 - [ 0.0301973834+ 0.105690842]

= 0.8641117746

≈ 0.864

(b) at most 1 accident in the next month?

= λ^x × e^-λ/x!

λ = 3.5

x = at most 1 such accidents

x ≤ 1

= [P(x = 0) + P(x = 1)]

= [(3.5^0 × e^-3.5/0!)+ (3.5^1 × e^-3.5/1!)]

= [ (1 × 0.0301973834) + (3.5 × 0.0301973834)]

[ 0.0301973834+ 0.105690842]

= 0.1358882254

≈ 0.136

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.