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Romashka-Z-Leto [24]
3 years ago
13

In a class of 25 students, 20 have a brother and 8 have a sister. There are 3 students

Mathematics
1 answer:
kaheart [24]3 years ago
6 0

Answer: 6/8 or 3/4 or 0.75

Step-by-step explanation:

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(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
A winter resort took a poll of its 400 visitors to see which winter activities people enjoyed. The results were as follows: 188
VARVARA [1.3K]
Exactly one activity:  246
None of the activities :  1
At least one activity:  74
Snowboarding and Ice skating but not skiing:  5
Snowboarding or ice skating but not skiing:  132.
Only skiing :  119.
The diagram is in the attachment. 
Download docx
6 0
3 years ago
A library wants to add a rectangular window made of small
Iteru [2.4K]

Answer:

A) 54

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well, first thing's first: find the area.

The formula for area is L*W

L=9 ft

W=6 ft

9*6=54 sq ft

Since the area is 54 sq ft, and each small glass square is 1 sq ft, you would need A) 54 squares of glass

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

3 0
3 years ago
Read 2 more answers
An analysis of the decay of 10 grams of an unstable element over time was completed and is displayed in the computer output.
Lady bird [3.3K]

The equation of the least-squared regression line is: In(Element) = 2.305 - 0.101(Time).

<h3>What is a regression line?</h3>

A regression line displays the connection between scattered data points in any set. It shows the relation between the dependent y variable and independent x variables when there is a linear pattern.

According to the given problem,

From the table we can see,

ln(Element) is the dependent variable and Time is the independent variable.

The constant = 2.305,

Time = -0.101

Hence, we can conclude, our least squared regression line will be

In (Element) = 2.305 - 0.101 (Time).

Learn more about regression line here: brainly.com/question/7656407

#SPJ2

6 0
2 years ago
What is the value of the expression?
Lady bird [3.3K]

Answer:

690

Step-by-step explanation:

(323+1715)-(1135+213)

(2038)-(1348)

=690

5 0
3 years ago
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