Answer:
(1) Yes, because 30 American citizens were sampled.
(2) The probability that the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35% is 0.50.
Step-by-step explanation:
We are given that from a representative list of 20677 American citizens, they randomly sampled 30; all responded to their questions.
Previously, 35% of Americans considered climate change an immediate threat to humanity; assume this has not changed.
(1) Yes, it is appropriate to use a normal distribution to describe the sampling distribution of sample proportion because 30 American citizens were sampled.
(2) The z-score probability distribution for the sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of Americans who agree climate change is an immediate threat to humanity
p = population proportion of Americans who considered climate change is an immediate threat to humanity
n = sample of American citizens = 30
Now, the probability that the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35% is given by = P([tex]\hat p[/tex] > 35%)
P([tex]\hat p[/tex] > 35%) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] > [tex]\frac{0.35-0.35}{\sqrt{\frac{0.35(1-0.35)}{30} } }[/tex] ) = P(Z > 0) = 0.50
The above probability is calculated by looking at the value of x = 0 in the z table which has an area of 0.50.
Hence, the required probability is 0.50.
Using the normal distribution and the central limit theorem, it is found that:
1. a. Yes, because 10.5 and 19.5 are greater than 10.
2. There is a 0.5 = 50% probability the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35%.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem:
A sample of 30 is taken, hence n = 30.35% of Americans considered climate change an immediate threat to humanity; assume this has not changed, hence p = 0.35.Item 1:
We verify the condition, hence:
[tex]np = 30(0.35) = 10.5[/tex]
[tex]n(1 - p) = 30(0.65) = 19.5[/tex]
Hence option a is correct.
Item 2:
The mean and the standard error are given by:
[tex]\mu = p = 0.35[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.35(0.65)}{30}} = 0.087[/tex]
The probability is 1 subtracted by the p-value of Z when X = 0.35, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.35 - 0.35}{0.087}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5.
1 - 0.5 = 0.5.
0.5 = 50% probability the proportion of the 30 Americans sampled that agree climate change is an immediate threat to humanity exceeds 35%.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
What is the sum or differece
-12 1/2 + 4 1/2
Answer:
-8
Step-by-step explanation:
What is the meaning of this notation, f^-1(x)?
Answer:
Notation. The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". ... The inverse of a function does not mean the reciprocal of a function.
Step-by-step explanation:
I hope this helps you!
The bill for the repair of your car was $597. The cost for parte was $268. The cost for labor was $47 per hour. How many hours did the repair work take?
Answer:
7 hours
Step-by
In 1982 John Hinckley was on trial, accused of having attempted to kill the then US President Ronald Reagan. Hinckley was found not guilty by reason of insanity. The defense psychiatric reports found him to be insane while the prosecution reports declared him legally sane. In particular, the defense sought to establish that brain scan results like John Hinckley's appeared in a higher percentage of schizophrenics than of normal people his age.
During Hinckley's trial, an expert witness, Dr. Weinberger, told the court that when individuals suffering from schizophrenia were given computerized axial tomography (CAT) scans, the scans showed brain atrophy in 30% of cases compared with only 2% of scans done on normal people. Health records show that 1.5% of the people in the United States suffer from schizophrenia. Hinckleys CAT scan showed brain atrophy. Calculate the probability that Hinckley suffered from schizophrenia given his CAT scan showed brain atrophy.
Answer:
O.186 or 18.6%
Step-by-step explanation:
Let s = event of schizophrenia
B = brain atrophy
From our question we have:
P(s) = probability of those suffering from schizophrenia = 1.5% = 0.015
P(B|S) = probability of brain atrophy = 30% = 0.30
P(S') = 1 - 0.015 = 0.985
P(B|S') = 2% = 0.02
Probability Hinckley suffered from schizophrenia
= P(S|B) = P(B|S)P(S)/P(B|S)P(S)+P(B|S')P(S')
= (0.30x0.015)/(0.30)*(0.015)+(0.02)(0.985)
= 0.0045/0.0045+0.0197
= 0.0045/0.0242
= 0.185950
This is approximately 0.186 or 18.6%
what is the quolotient of the division below
96÷3
answers: 13 23 31 42
Answer: The answer would be 32
Step-by-step explanation: 96 divided by 3 is 32
A pipe is 30 feet long. It needs to be cut into pieces that are each 3/5
feet long. How many pieces can be made from the pipe?
Answer:
The answer is 50
Step-by-step explanation:
30 divided by 3/5= 50
Find the value of x in the equation below.
17 = 14 +2
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
17 = 14 + x
x = 17 - 14
x = 3
What is the slope of the line through (-3, 3) and (-1, -1)?
Answer:
[tex]m=-2[/tex]
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Simply plug in the 2 coordinates into the slope formula to find slope m:
[tex]m=\frac{-1-3}{-1-(-3)}[/tex]
[tex]m=\frac{-4}{-1+3}[/tex]
[tex]m=\frac{-4}{2}[/tex]
[tex]m=-2[/tex]
Identify the domain and range of the relation. {(-9,2), (-4, 2), (3, 2), (9,2)
Answer:
Domain: - 9, - 4, 3, 9
Range: 2
Step-by-step explanation:
The domain is the first coordinate of an ordered pair. This means that the domain is going to be x. The range is the second coordinate of an ordered pair. This means that the range is going to be y. Since all of the second coordinates are 2 you only have to put 2 once. The domain of the set of ordered pairs is - 9, - 4, 3, 9.
Hope This Helps :)
Saved
Find all solutions of 5−4 secx = −3 on the interval [0, 2π).
Answer:
[tex]\theta=\dfrac{\pi }{3}\\\\\theta=\dfrac{5\pi }{3}[/tex]
Step-by-step explanation:
[tex]\theta = x[/tex]
[tex]5-4 \sec (\theta) = -3[/tex]
[tex]-4 \sec (\theta) = -3-5[/tex]
[tex]-4 \sec (\theta) = -8[/tex]
[tex]\dfrac{-4 \sec (\theta)}{-4} =\dfrac{-8}{-4}[/tex]
[tex]\sec (\theta)=2[/tex]
Once
[tex]\sec(\theta)=\dfrac{1}{\cos(\theta)}[/tex]
[tex]\sec (\theta)=2 \implies \dfrac{1}{\cos(\theta)}=2 \implies \cos(\theta)=\dfrac{1}{2}[/tex]
The solutions for [tex]\cos(\theta)=\dfrac{1}{2}[/tex] are
[tex]\theta=\dfrac{\pi }{3}+2\pi n, n \in \mathbb{Z}\\\\\theta=\dfrac{5\pi }{3}+2\pi n, n \in \mathbb{Z}[/tex]
But once the interval for the solution was given,
For [tex][0, 2\pi)[/tex]
[tex]\theta=\dfrac{\pi }{3}\\\\\theta=\dfrac{5\pi }{3}[/tex]
please help with these! or at least some of them.
Answer:
1) 9/2 = 5/45) False6) $667) x=78) x=69Step-by-step explanation:
How is multiplying complex numbers different
from adding or subtracting complex numbers?
Let P and Q be two complex numbers such that
P = a+bi
Q = c+di
Where a,b,c,d are real numbers and i = sqrt(-1).
This means i^2 = -1.
-------------------
Adding P and Q means
P+Q = (a+bi)+(c+di)
P+Q = a+bi + c+di
P+Q = (a+c) + (bi+di)
P+Q = (a+c) + (b+d)i
As you can see, we just add the corresponding components together.
-------------------
Subtraction is a similar story.
P-Q = (a+bi)-(c+di)
P-Q = a+bi - c-di
P-Q = (a-c) + (bi-di)
P-Q = (a-c) + (b-d)i
We subtract the corresponding components
-------------------
Multiplication is a bit more complicated.
We'll use the FOIL rule
P*Q = (a+bi)*(c+di)
P*Q = a*c + a*di + bi*c + bi*di
P*Q = a*c + ad*i + bc*i + bd*i^2
P*Q = a*c + ad*i + bc*i + bd*(-1)
P*Q = a*c + ad*i + bc*i - bd
P*Q = (ac - bd) + (ad*i + bc*i)
P*Q = (ac - bd) + (ad + bc)i
Unfortunately multiplication isn't as simple as addition or subtraction, but we can at least make a tidy formula for it. You could also use the box method to visually organize the terms into a table to help multiply out P and Q.
Answer:
because they have different stepa
Brad, a teenager, saves up his monthly allowance over a period of six months to buy a
pair of high-resolution headphones. He lends his friend, Jorge $10 from his savings. If
Brad has $272 now, calculate his monthly allowance.
I
Answer:
$43.7
Step-by-step explanation:
272-10/6
272-10=262
262/6=43.66666=43.7
The amount of monthly allowance of Brad will be $43.67 per month.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Brad, a teenager, saves up his monthly allowance over a period of six months to buy a pair of high-resolution headphones. He lends his friend, Jorge $10 from his savings. If Brad has $272 now.
Then a monthly allowance of Brad will be given as,
⇒ ($272 - $10) / 6
⇒ $262 / 6
⇒ $43.67
The amount of monthly allowance of Brad will be $43.67 per month.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
Dacă aș avea 4 ouă Un hoț îmi dă 3 ouă Cocoșul meu de fermă depune 5 ouăCâte ouă am?
Answer:
Step-by-step explanation:
3 oua
Daca as avea 4 oua - e presupunere. Nu am.
Un hot imi da 3
Cocosul nu face oua
0+3+0=3
Michael lives 2 3/5 miles away from the school Sarah lives 1/2 as long as Michael how far does Sarah live from the school
Answer:
Let's see what to do buddy...
Step-by-step explanation:
[tex]2 \frac{3}{5} miles = \frac{10}{5} + \frac{3}{5} \: miles = \frac{13}{5} \: miles \\ [/tex]
So Michael lives 13/5 miles away from the school.
_________________________________
Sarah lives 1/2 as long as Michael.
So the distance from the school of where Sarah's house located is 1/2 distance from the school of where Michael's house located.
Which means :
[tex] \frac{13}{5} \div 2 = \frac{13}{5} \times \frac{1}{2} = \frac{13}{10} \\ [/tex]
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
I’ll give brainly thingy please help me
Answer:
20%
Step-by-step explanation:
You would have to add 1200 and 300 to get the total amount of students which would be 1500.
Then put 1500 as the denominator and 300 as the numerator since we're talking about the number of students that did NOT wear their school colors. our fraction should then be 300/1500.
If you cross out 2 zeros on both numbers, you'll get 3/15. if you reduce that you get 1/5. 1/5= 20%
A square has area of 9 yd squared. What is the length of both sides?
Answer:
Each side is 3 yds
Step-by-step explanation:
The area of a square is given by
A = s^2
9 = s^2
Take the square root of each side
sqrt(9) = sqrt(s^2)
3 = s
Each side is 3 yds
what is the measure of B, in degrees?
Answer:
D, 32 degrees
Step-by-step explanation:
Someone Please help me with this with Step by Step explanation.
there you go i think thats it
Find the midpoint between each pair of points. (-1, -5) and (-5, 9)
Answer:
[tex](-3,2 )[/tex]
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )[/tex]
Simply plug in your coordinates into the midpoint formula to find midpoint:
[tex](\frac{-1-5}{2},\frac{-5+9}{2} )[/tex]
[tex](\frac{-6}{2},\frac{4}{2} )[/tex]
[tex](-3,2 )[/tex]
Please help me!!! I will make you brainiest!!! How does the graph of y=2x+4 compare to the graph of y=x+4
Answer:
ALGUIEN PARA COJER?
TENGO 20 PERRO
Answer:
c
Step-by-step explanation:
Sixty students are invited to an Hono Roll Pizza Party. There are 24
sodas in a package and 18 slices per pizza. What is the least number of
packages of soda and pizzas that can be bought if each person gets
one soda and one slice of pizza?
Answer:
2.5 boxes of soda or round it to 3
3.3 boxes of pizza or round it to 4
If a dozen eggs costs $2.50, how much does 1 egg cost?
Answer:
The cheapest eggs you'll find can cost as little as 59 cents.
Step-by-step explanation:
Hope that helped :)
devaughn’s age is three times Sydney’s age. The sum of their age is 100. What is Sidney’s age?
Answer:
the answer is 300
Step-by-step explanation:
I'm 95% sure
Which of the following most clearly defines an undefined geometric object? (Click picture).
Answer:
A is the correct answer
Kevin went to see his favorite sport team play. His car can go 320 miles on one tank of gas. If he used 50% of a full tank of gas how many miles will he travel
Answer:
To find the percentage of something you must multiply it by that number divided by 100. So if it were 25% then you would times 300 by 0.25.
in this case though it is 40% of three hundred, so you would make it a decimal and times 300 by 0.4. which would result in 120 miles
Step-by-step explanation:
YOUR WELCOME :)
WhY DiD ThE LiTlE PiG Go AlL ThE WaY HOmE
At an educational institution, the cost of room and board includes
Answer:
what are you trying to ask
Step-by-step explanation:
Answer:
A: housing and meal
Step-by-step explanation:
Edg 2021
took the test
I need help with this
Answer:
see attached
Step-by-step explanation:
The domain is the horizontal extent of the graph. The graph extends to infinity in both directions horizontally (that's what the arrows mean). There are no "holes" because the open circle at x=-1 is matched by a filled circle at the same location.
__
The range is the vertical extent of the graph. The minimum is -3, which is included in the range. The maximum is infinity (as indicated by the up-pointing arrow).
In how many ways can we write a number using the digits (0,2,3,5) and the number is greater than 100
This is a multiplicative principle's question. Let's think how we can solve that.
If we want numbers are greater than 1000, so we need numbers with 4 digit (for example: 1001, 2350 and so on).
Imagine that we need to complete four spaces: one thousands, hundreds, tens and ones. See below how to compelete each space:
One thousands: In this space, we can't use the number 0, because in this way, the number will have 3 digits and we want number with 4 digits (for example: 0235 is a 3 digits number). Therefore, we can use the numbers 2, 3 and 5 to complete this space. So, there are 3 possibilities.Hundreds: Now, we can use the number 0 and the number won't have 3 digits (for example: 2035 is a 4 digits number). Therefore, we can use the numbers 0, 2, 3 and 5 to complete this space. So, there are 4 possibililities.Tens: Ih this case, it happens the same thing that happen in the case of hundreds. Therefore, there are 4 possibilites.Ones: Finally, in this case it also happens the same thing that happen in the case os hundreds. So, there are 4 possibilites.For multiplicative principle, we just need multiply these numbers of possibilities to find the result of this question:
[tex]3\times4\times4\times4=192[/tex]
Therefore, we can write 192 numbers using the digits (0, 2, 3 and 5) and all these numbers are greater than 1000.