Let's say you want to poll a random sample of 150 students on campus to see if they prefer to take online classes. Of course, if you took an actual poll you would only get one number (your sample proportion, p-hat). Imagine all the possible samples of 150 students that you could draw and the distribution of all the possible sample proportions you would get from them.
If I told you that we know that 35% of all students actually prefer to take classes online, how would you respond to the following?:
1. Discuss the conditions necessary to use the normal curve to model this sampling distribution and explain whether or not they are met.
2. If the normal model is appropriate for this distribution, what shape would you expect it to have?
3. If you were to use the normal model for this p-hat sampling distribution, what value would be at the center of your sampling distribution? In other words, what value would all of those sample proportions center around?
4. What would be the standard deviation of this sampling distribution?

Answers

Answer 1

Answer:

1. Since [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], these conditions are met.

2. Approximately normal.

3. 0.35

4. 0.0389

Step-by-step explanation:

Central Limit Theorem:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be 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]

Let's say you want to poll a random sample of 150 students on campus to see if they prefer to take online classes.

This means that [tex]n = 150[/tex].

35% of all students actually prefer to take classes online

This means that [tex]p = 0.35[/tex]

1. Discuss the conditions necessary to use the normal curve to model this sampling distribution and explain whether or not they are met.

The conditions necessary are [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].

We have that

[tex]np = 150*0.35 = 52.5 \geq 10[/tex]

[tex]n(1-p) = 150*0.65 = 97.5 \geq 10[/tex]

Since [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], these conditions are met.

2. If the normal model is appropriate for this distribution, what shape would you expect it to have?

By the Central Limit Theorem, approximately normal.

3. If you were to use the normal model for this p-hat sampling distribution, what value would be at the center of your sampling distribution? In other words, what value would all of those sample proportions center around?

The mean, which by the Central Limit Theorem, is [tex]\mu = 0.35[/tex].

4. What would be the standard deviation of this sampling distribution?

By the Central Limit Theorem,

[tex]s = \sqrt{\frac{0.35*0.65}{150}} = 0.0389[/tex]


Related Questions

What is the volume of the cylinder?


384 cm3

14 cm3

288 cm3

48 cm3

Answers

Answer/Step-by-step explanation:

Volume of a cylinder is given as V = πr²h

Where,

radius (r) = 6 cm

height (h) = 8 cm

Plug in the values

V = π*6²*8

V = π*36*8

V = π*288

V = 288π cm³ or 904.78 cm³

What is the domain of the relation graphed below?

Answers

Answer:

Domain: {-5, -4, -3, 1, 2, 5}

Step-by-step explanation:

Recall:

Domain = inputs (x-values)

Range = outputs (y-values)

All set of x-values (input) of the points that are plotted on the graph make up the domain of the relation.

Thus, they are:

Domain: {-5, -4, -3, 1, 2, 5}

body fat of 13.5% and weighs 166 pounds. How many pounds of his weight is made up of fat? ​

Answers

Answer:

22.41

Step-by-step explanation:

100%-> 166

13.5%-> 22.41

Sanjay, Ajay and Anushka are employees of a company that has branches in Chennai, Bangalore and Mumbai. The company sends each of them to one of these cities at random. Let X X be a random variable that denotes the number of employees assigned to their favourite cities. If Chennai, Bangalore and Mumbai are the favourite cities of Sanjay, Ajay and Anushka, respectively, then find the possible values of X.

a. X= {0,1,2}
b. X= {0,1,2,3}
c. X= {0,1,3}
d. X= {0,[infinity]}

Answers

Answer:

c. X= {0,1,3}

Step-by-step explanation:

We have these possible outcomes:

None assigned to their favorite cities.

One assigned to their favorite city(The other two are assigned to the other's favorite city).

All are assigned to their favorite city.

Why is two not possible?

If two peooke are assigned to their favorite city, the third person necessary has to be assigned to their favorite city, as it will be the only option remaining.

So the correct answer is given by option c.

Twice a number is 17

Answers

Answer:

Twice a number is 17=2×17=34

8.5

8.5=8.5=17

8+8=16

.5+.5=1

16+1=17

is 10a + 1b equivalent to 7a+5b-3a+4b
or
4a + 9b equivalent to 7a+5b - 3a +4b
explain plsss​

Answers

4a+9b , Because 7a-3a would be 4a, and 5b+4b= 9b

A graphing calculator is recommended. A bacteria culture starts with 300 bacteria and doubles in size every half hour. (a) How many bacteria are there after 2 hours? bacteria (b) How many bacteria are there after t hours? y = bacteria (c) How many bacteria are there after 40 minutes? (Round your answer to the nearest whole number.)

Answers

Answer:

a) 4800 bacteria

b) [tex]y(t) = 300(4)^t[/tex]

c) 754 bacteria

Step-by-step explanation:

A bacteria culture starts with 300 bacteria and doubles in size every half hour.

This means that the number of bacteria after t periods of half hour is given by:

[tex]y(t) = 300*(2)^{t}[/tex]

(a) How many bacteria are there after 2 hours?

2 hours is 2*60/30 = 4 periods of 2 hours, so this is y(4).

[tex]y(4) = 300*(2)^{4} = 300*16 = 4800[/tex]

(b) How many bacteria are there after t hours?

It doubles every half hour, so each hour, it is multiplied by 4. Then

[tex]y(t) = 300(4)^t[/tex]

(c) How many bacteria are there after 40 minutes?

40 minutes is 40/30 = 1.33 periods of half hour. So this is y(1.33).

[tex]y(1.33) = 300*(2)^{1.33} = 754[/tex]

Consider the diagram and the paragraph proof below.

Given: Right △ABC as shown where CD is an altitude of the triangle
Prove: a2 + b2 = c2

Triangle A B C is shown. Angle A C B is a right angle. An altitude is drawn from point C to point D on side A B to form a right angle. The length of C B is a, the length of A C is b, the length of A B is c, the length of A D is e, the length of D B is f, and the length of C D is h.

Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions StartFraction c Over a EndFraction = StartFraction a Over f EndFraction and StartFraction c Over b EndFraction = StartFraction b Over e EndFraction are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).

Which is the last sentence of the proof?

Because f + e = 1, a2 + b2 = c2.
Because f + e = c, a2 + b2 = c2.
Because a2 + b2 = c2, f + e = c.
Because a2 + b2 = c2, f + e = 1.

Answers

Answer:

I don't know how I can help you but I found this from another person. Hope this helps!

Answer:

The answer is b

Step-by-step explanation:

Consider the diagram and the paragraph proof below.

Given: Right △ABC as shown where CD is an altitude of the triangle

Prove: a2 + b2 = c2

 Triangle A B C is shown. Angle A C B is a right angle. An altitude is drawn from point C to point D on side A B to form a right angle. The length of C B is a, the length of A C is b, the length of A B is c, the length of A D is e, the length of D B is f, and the length of C D is h.

Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions StartFraction c Over a EndFraction = StartFraction a Over f EndFraction and StartFraction c Over b EndFraction = StartFraction b Over e EndFraction are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).

Which is the last sentence of the proof?

Because f + e = 1, a2 + b2 = c2.

Because f + e = c, a2 + b2 = c2.

Because  a2 + b2 = c2, f + e = c.

Because  a2 + b2 = c2, f + e = 1.

Which part of the water cycle is this image most similar to?

Answers

Collection or percolation

Can someone help me please help pls thank you so much

Answers

Answer:

B

Step-by-step explanation:

To answer this question, you simply have to keep track of the numbers given and make sure that there is an 'X' for each number where it belongs. By looking at the line plots, we can say that the answer is:

Chart B

Hope this helps :)

Solve for x and y. Please help, I will mark as brainliest and give many points

Answers

Answer:

x=13 y=25

Step-by-step explanation:

Answer:

x = 30°, y = 45°, w = 14√2, v = 7√2

Step-by-step explanation:

ΔABC has AB = 2BC, hypotenuse is twice the leg

⇒ x = 30°

ΔBCD is isosceles right triangle

⇒ y = 45°

ΔMPN is isosceles right triangle (∠M = 45°)

⇒ w = MN = √2PN = 14√2

ΔMKP is isosceles right triangle (∠M = 45°)

v= KP = MK = 1/2MN = 1/2(14√2) = 7√2


On a particularly rainy day the amount of rainfall measured in a rain gauge increased at a
rate of 1.5 inches each hour for 4 hours. What is the total change in the amount of rain that
has fallen after 4 hours?

Answers

The answer is 6 ! Because you do 4 x1.5 !

What is the value of n in 2n+1=3

Answers

2n+1=3
2n=3-1
2n=2
n=1 is the answer

Answer:

n=1

Step-by-step explanation:

2n+1-1=3-1

2n=2 divide both sides by two

n=1

 can i get brainliest please???

it would be very much appreciated

have a nice day :)

4(10-x)=40-4x is one solution

Answers

Answer:

( -infinity, infinity)

Step-by-step explanation:

any value of x is true

Help me with this one please, the highlighted one is wrong.

Answers

Answer:

d

Step-by-step explanation:

i did this before so i pretty much know

from the set 1/2/3/4/5 which values make the inequality n + 1 > true?

Answers

Hi there!

To make n+1>4 true, you must have n be a numebr greater than 3...

The reason why is because if it is less than 3 or 3, it’ll have to be <.

The two numbers that can make this equation true is 4 and 5...

[tex]4+1=5>4[/tex]

[tex]5+1=6>4[/tex]

And if it is 1,2, and 3 it would be:

[tex]1+1=2<4[/tex]

[tex]2+1=3<4[/tex]

[tex]3+1=4=4[/tex]

The school play earned $11,271 in ticket sales. If the cost of each ticket was $13, how many tickets were sold?

Answers

Answer:

867 tickets were sold because if you divide how much they earned by how much it cost you get 867

Answer:

867 Tickets

Step-by-step explanation:

Divide $11,271 by the number of the ticket cost $13.

11,271/13= 867

What is the y intercept of the line?


-3


1


5


-2

Answers

-3 is where the line hits the y axis, hope this helped

A picture-framing shop has the sign shown below in the window.

Frame Sale!

Half Off 17-inch-by-24-inch Frames

A customer has a 4-inch-by-6-inch picture. If the customer wants to enlarge the photograph so that it will come as close as possible to fitting a sale frame, how many times larger should the photo be?

A. 2
B. 3
C. 4
D. 5
E. 13

Answers

Answer:

This answer should help it will be in the comments side

Step-by-step explanation:

factor this polynomial x^2 -3x^3 +10x^7

Answers

x^2 (1-3x+ 10x^5)
pls mark brainliest if correct

which function defines (f divided by g)(x)

Answers

Answer:

A if its wrong im sorry

Step-by-step explanation:

The function is (f ÷ g) (x) is given as [tex](3.6)^{-2x + 1}[/tex]. Then the correct option is A.

What is a function?

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The functions are given as

[tex]\rm f(x) = (3.6)^{x + 2}\\\\\\g(x) = (3.6)^{3x + 1}[/tex]

The f(x) is divided by the g(x), we have

[tex]\rm (f \div g ) (x) = \dfrac{f(x)}{g(x)} = \dfrac{(3.6)^{x + 2}}{(3.6)^{3x + 1}}\\\\\\(f \div g ) (x) = (3.6)^{x + 2}*(3.6)^{-(3x + 1)}\\\\\\(f \div g ) (x) = (3.6)^{x + 2- 3x - 1}\\\\\\(f \div g ) (x) = (3.6)^{-2x + 1}[/tex]

More about the function link is given below.

https://brainly.com/question/5245372

(24 points) Need some help please !

Answers

Answer:

39°

Step-by-step explanation:

3x+15+1+10x+60=180

13x+76=180

13x=180-76

13x=104

x=8

A=3x+15

A=3(8)+15

A=24+15

A=39

An advertising agency notices that approximately 1 in 50 potential buyers of a product ssees a given magazine ad, and 1 in 5 sees a corresponding ad on television. One in 100 see both. One in 3 actually purchases the product after seeing the ad, 1 in 10 without seeing it. What is the probability that a randomly selected potential customer will purchase the product

Answers

Answer:

0.1490 = 14.90% probability that a randomly selected potential customer will purchase the product.

Step-by-step explanation:

Probability of seeing the ad:

I am going to find this probability using Venn Sets.

I am going to say that:

Event A: Sees a magazine ad.

Event B: Sees a television ad.

Approximately 1 in 50 potential buyers of a product sees a given magazine ad

This means that [tex]P(A) = \frac{1}{50} = 0.02[/tex]

1 in 5 sees a corresponding ad on television.

This means that [tex]P(B) = \frac{1}{5} = 0.2[/tex]

One in 100 see both.

This means that [tex]P(A \cap B) = \frac{1}{100} = 0.01[/tex]

The probability of seeing the ad is the probability of seeing at least one of those(magazine or tv), which is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]. So

[tex]P(A \cup B) = 0.2 + 0.02 - 0.01[/tex]

[tex]P(A \cup B) = 0.21[/tex]

Probability of purchasing the product.

0.21 = 21% of customers see the add. Of those, 1/3 = 0.3333 buy the product.

1 - 0.21 = 0.79 = 79% of customers dont see the add. Of those, 1/10 = 0.1 buy the product. So

[tex]p= 0.21*0.3333 + 0.79*0.1 = 0.1490[/tex]

0.1490 = 14.90% probability that a randomly selected potential customer will purchase the product.

Find the slope given: (1,5) & (3,12)
m =

Answers

Answer:

Rise (y) over Run (x)

12-5

------

3-1

7/2=m

Step-by-step explanation:

Answer:

[tex]\frac{7}{2}[/tex]

Step-by-step explanation:

Slope, or the Rise/run formula is typically used on the coordinate plane to figure the equation of a line. Although we are not given the direct image, we can still determine the slope by using the following formula:

[tex]slope=\frac{rise}{run} =\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\=\frac{12-5}{3-1} \\=\frac{7}{2} \\slope=\frac{7}{2}[/tex]

I would be ahppy to help you again in the future, and hope that this answer gives you some clarification :D

How do you work 6x²-2=11x

Answers

X= -1/6, 2
Hope that helps

Answer:

Step-by-step explanation:

Please be specific:  "How do you solve 6x^2 - 2 = 11x?"

Rewrite this in terms of descending powers of x:  6x^2 - 11x - 1 = 0.

Use the quadratic formula to find the roots.  Here the coefficients are a = 6, b = -11 and c = -1.  Then the discriminant b^2 - 4ac becomes 121 - 4(6)(-1) = 121 + 24 = 145, and so the roots are:

       -(-11) ± √145          11 ± √145

x = ---------------------- = ------------------

             2(6)                       12

Lluvia got $100 from her grandparents for her birthday. She has a weekly after school babysitting job. She earns $40 per week from her babysitting job.

A. If she does not spend any of her money, write an algebraic expression that shows how much money she has after w weeks.
B. How much money will she have after 10 weeks.
C. Alex thinks the expression 10 (40w + 10) is represents the. total amount of money Lluvia will have after w weeks. Explain whether or not Alex is correct.

Answers

Answer:

A. Y= 40w+100

B.  $500

C. That would make her $400 per week plus the 100 dollars from her grandparents

Step-by-step explanation:

(6x - 3y) -2(x + 4y)

Answers

Answer:

4x-11y

Step-by-step explanation:

How to solve your question

Simplify

(6−3)−2(+4)

(6x-3y)-2(x+4y)

(6x−3y)−2(x+4y)

Distribute

(6−3)−2(+4)

(6−3)−2−8

Eliminate redundant parentheses

(6−3)−2−8

6−3−2−8

Combine like terms

6−3−2−8

4−3−8

Combine like terms

4−3−8

4−11

What is the area of the triangle?

Answers

Step-by-step explanation:

4x6= 24

answer: 24

GOOD LUCK ON YOUR TEST

I will give 15 points and brainliest for this answer

Answers

Here is your answer:

What is 4x - 8x + 11 + 24

Answers

the answer is -4x+35
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