We are throwing darts on a disk shaped board of radius 5. We assumethat the position of the dart is a uniformly chosen point in the disk. The board hasa disk shaped bullseye with radius 1. Suppose that we throw a dart 2000 times atthe board. Estimate the probability that we hit the bullseye at least 100 times.

This is an example of a Binomial distribution, in which the chance of striking the dart here on the disc is:

Since this is a huge figure, one can use the central limit theory to approximate a supplied binomial distribution to a normally distributed one. As just a result, you have:

Since this is    a huge figure, one can use the central limit theory to approximate a supplied binomial distribution to a normally distributed one. As just a result, you have:

We must now calculate the likelihood of hitting the bullseye at least 100 times:

When we convert this to a conventional normal variable, we get:

When we use the conventional normal table to calculate this probability, we get:

Therefore the required probability is "0.0112".

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5% is the smallest probability

Step-by-step explanation:

5% = 0.05

2000 x 0.05 = 100 so the smallest chance is 5% but it could be more if you hit more bullseye

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.