How to find the area of an equilateral triangle inside a circle

(43 points) In the US, 85% of the population has Rh positive blood. Suppose we take a random sample of 6 persons and let Y denot

VladimirAG [237]

Answer:

a) Binomial distribution with parameters p=0.85 q=0.15 n=6

b) 62.29%

c) 2.38%

d) See explanation below

Step-by-step explanation:

a)

We could model this situation with a binomial distribution

$P(6;k)=\binom{6}{k}p^kq^{6-k}$

where P(6;k) is the probability of finding exactly k people out of 6 with Rh positive, p is the probability of finding one person with Rh positive and q=(1-p) the probability of finding a person with no Rh.

So

$\bf P(Y=k)=\binom{6}{k}(0.85)^k(0.15)^{6-k}$

b)

The probability that Y is less than 6 is

P(Y=0)+P(Y=1)+...+P(Y=5)

Let's compute each of these terms

$P(Y=0)=P(6;0)=\binom{6}{0}(0.85)^0(0.15)^{6}=1.139*10^{-5}$

$P(Y=1)=P(6;1)=\binom{6}{1}(0.85)^1(0.15)^{5}=0.0000387281$

$P(Y=2)=P(6;2)=\binom{6}{2}(0.85)^2(0.15)^{4}=0.005486484$

$P(Y=3)=P(6;3)=\binom{6}{3}(0.85)^3(0.15)^{3}=0.041453438$

$P(Y=4)=P(6;4)=\binom{6}{4}(0.85)^4(0.15)^{2}=0.176177109$

$P(Y=5)=P(6;5)=\binom{6}{5}(0.85)^5(0.15)^{1}=0.399334781$

and adding up these values we have that the probability that Y is less than 6 is

$\sum_{i=1}^{5}P(Y=i)=0.622850484\approx 0.6229=62.29\%$

c)

In this case is a binomial distribution with n=200 instead of 6.

p and q remain the same.

The mean of this sample would be 85% of 200 = 170.

In a binomial distribution, the standard deviation is

$s = \sqrt{npq}$

In this case

$\sqrt{200(0.85)(0.15)}=5.05$

<em>Let's approximate the distribution with a normal distribution with mean 170 and standard deviation 5.05</em>

So, the approximate probability that there are fewer than 160 persons with Rh positive blood in a sample of 200 would be the area under the normal curve to the left of 160

(see picture attached)

We can compute that area with a computer and find it is

0.0238 or 2.38%

d)<em> In order to approximate a binomial distribution with a normal distribution we need a large sample like the one taken in c).</em>

In general, we can do this if the sample of size n the following inequalities hold:

$np\geq 5 \;and\;nq \geq 5$

in our case np = 200*0.85 = 170 and nq = 200*0.15 = 30

4 0

3 years ago

Count by tens and ones to find the sum.use the number line to show your thinking 86.

mojhsa [17]

To get to 86 by only using 10's and 1's you count by 10, 8 times and count by 1, 6 times.

5 0

3 years ago

Please help me

morpeh [17]

Answer:

No, because the cone has a smaller volume than the ice cream

Step-by-step explanation:

V=4

3πr3=4

3·π·33≈113.09734

Volume of scoop: 113.1 cm^2

V=πr2h

3=π·2.52·10

3≈65.44985

Volume of cone: 65.45 cm^2

65.45 < 113.1

6 0

2 years ago

Name the property illustrated in this statement. If y - 2 = -8. then y - 2 + 2 = -8 + 2.

Gennadij [26K]

10

Step-by-step explanation:

first what is 10 take away 2 is 8 then 10 take away 2 is 8 + 2 equals 10 8 + 2 equals 10 so that's how I got the answer 10

4 0

3 years ago

Which is the height of the triangle?<br> ( PIC IS PROVIDE PLS HELP ME)

zysi [14]

<h3>Answer: 80 meters</h3>

This is an isosceles triangle. The dashed line is the height which is perpendicular to the base 120. The height is always perpendicular to the base. The dashed line cuts the base into two equal pieces (this only works for isosceles triangles when you cut at the vertex like this).

So we have two smaller triangles each with a base of 60 and a height of x. Focus on one of the right triangles and use the pythagorean theorem to solve for x.

a^2 + b^2 = c^2

x^2 + (60)^2 = (100)^2

x^2 + 3600 = 10000

x^2 = 10000 - 3600

x^2 = 6400

x = sqrt(6400)

x = 80

Each smaller right triangle has side lengths of 60, 80, 100

Note the ratio 60:80:100 reduces to 3:4:5. A 3-4-5 right triangle is a very common pythagorean primitive.

5 0

3 years ago

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