1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sergeinik [125]
3 years ago
12

(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

e the number of persons, out of 6, with Rh positive blood. a. (7 points) What is the distribution of Y ? Please name the distribution and provide the parameter values for the distribution. b. (10 points) What is the probability that Y is less than 6? c. (20 points) Suppose 200 persons are randomly selected from the US population. What is the approximate probability that there are fewer than 160 persons with Rh positive blood in a sample of 200? d. (6 points) State the large sample assumptions needed in (c).

Mathematics
1 answer:
VladimirAG [237]3 years ago
4 0

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

You might be interested in
Find the sum: 35,076 + 6,825 = ______.
Tcecarenko [31]
41,901




that’s the answer
5 0
2 years ago
Read 2 more answers
Find the sum and product of the roots. 3x^<br> 2 - 4x - 7 = 0
victus00 [196]
Given the quadratic function, to get the roots we factorize:
3x²-4x-7=0

3x²+3x-7x-7=0
3x(x+1)-7(x+1)=0
(3x-7)(x+1)=0
thus the roots are
x=-1 or x=3/7
thus the sum of the roots will be:
-1+3/7
=-4/7
6 0
3 years ago
0.30 meters is equal to 1 what
liberstina [14]
0.30 meter is equal to 1 foot
8 0
3 years ago
Please help! algebra 1 math! whoever gets right is Brainliest! (10 points)
leva [86]

multiply the 2/3 x the 1/6 to get 1/9

 so the original equation can be rewritten as 3^1/9

 this can be rewritten as the 2nd choice 9cubed3

8 0
3 years ago
If f(x)=1−x^2 +x^3 , then f(−1)=
Andrews [41]

Answer:

f(-1) = -1

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Functions
  • Function Notation

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

f(x) = 1 - x² + x³

f(-1) is <em>x</em> = -1 for the function f(x)

<u>Step 2: Evaluate</u>

  1. Substitute in <em>x</em> [Function f(x)]:                                                                           f(-1) = 1 - (-1)² + (-1)³
  2. Exponents:                                                                                                        f(-1) = 1 - 1 - 1
  3. Subtract:                                                                                                            f(-1) = -1
6 0
3 years ago
Other questions:
  • 3. Repeat Exercises 1 and 2 to obtain a second sample of 40 coin flips.
    8·1 answer
  • Can someone help me with one more pls I’ll comment on yours
    10·1 answer
  • june madera a de singular with 6 equilibrio tiles. one tiles is y ellos, 2 tiles are blue, and 3 tiles are purple
    9·1 answer
  • What is 0 + y, when y = -12
    8·2 answers
  • (n^(4))/(n^(4)) what does that equal?
    13·1 answer
  • 38/12 what is it in cents and dollars
    12·1 answer
  • A bank account pays 4.2% interest.write an equation with an intial value 2000.how much will the account have in it after 5 years
    9·1 answer
  • What is 567x39 and how do you solve it thank you
    9·2 answers
  • Is 3/2 the opposite of 6/4 on a number line? Please I’m so bad at this
    10·2 answers
  • I NEED HELP ASAP!!!!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!