A study conducted by the Center for Disease Control that asked 15,000 students about
their sleep habits showed that about 73% of high school students did not get the
required 8 hours of sleep per night. Let p be the proportion of high school students who
do not get 8 hours of sleep daily.
What is the sampling distribution of p?

Answers

Answer 1

Answer:

The sampling distribution of [tex]\hat p[/tex] is: [tex]\hat p\sim N(p,\ \frac{p(1-p)}{n})[/tex].

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

[tex]\mu_{\hat p}=p[/tex]

The standard deviation of this sampling distribution of sample proportion is:

[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]

The study was conducted using the data from 15,000 students.

Since the sample size is so large, i.e. n = 15000 > 30, the central limit theorem is applicable to approximate the sampling distribution of sample proportions.

So, the sampling distribution of [tex]\hat p[/tex] is: [tex]\hat p\sim N(p,\ \frac{p(1-p)}{n})[/tex].


Related Questions

HELP I DON'T WANNA GET THIS ONE WRONG
Which letter has rotational symmetry?

A. Q
B. H
C. G
D. A

Answers

Answer: (B). H

Step-by-step explanation:

Got it ?

Yesterday, between noon and midnight, the temperature went down by 32.1°F. If the temperature was -6.6°F at midnight, what was it at noon?

Answers

Answer:

25.5°F

Step-by-step explanation:

²3¹¹2.¹1

     6.6     -                      Bold means that its supposed to have a strikethrough   2  5.5                               meaning the number is being cancelled

just take 6.6 away from 32.1

please help me this is due soon!! ill mark brainiest :))
i also need a reason why please!!

Answers

Answer:

b

Step-by-step explanation:

One square = (2/5)/(3) Invert and multiply the 3

2      1

==    ==    =

5       3

2/15

5 squares = 5 * 2/15 = 10 / 15 = 2/3

Which property is illustrated by the equation 6+(4+x)=6+(x+4)?

1.) Associative property of addition 2.) Associative property of multiplication
3.) Distributive Property 4.) Commutative property of addition

Answers

1. Associative property of addition

The property illustrated by the equation 6 + (4 + x) = 6 + (x + 4) is the commutative property of addition.

The commutative property of addition states that the order in which numbers are added does not affect the result. In this equation, both sides of the equation involve adding numbers, and the numbers being added are the same: 6, 4, and x.

The equation shows that regardless of whether we add 4 and x first or x and 4 first within the parentheses, the final result will be the same. The commutative property of addition allows us to freely rearrange the order of the terms being added without changing the overall sum.

Therefore, The property illustrated by the equation 6 + (4 + x) = 6 + (x + 4) is the commutative property of addition.

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What numbers would be in the in the 4 sections of a 2 x 2 array that shows the problem 18 x 17? 100, 80, 70, 15 10, 80, 70, 56 100, 80, 70, 56 100, 80, 7, 56

Answers

Answer:

100, 70, 80, 56

Explanation:

Look at attached image!

In the 2 x 2 array, the sum of all squares is 18 x 17 = 306.

The number in the 4 sections are 100, 80, 70, and 56.

A 2 x 2 array that shows the problem 18 x 17.

2 x 2 array has four blockers or magic quadrants, the matrix diagram is a simple square divided into four equal quadrants.

18 = 10 +8

17 = 10 +7

18 x 17 = 306

In the 2 x 2 array : 100+80+70+56 = 18 x 17 = 306

Therefore, In the 2 x 2 array, the sum of all squares is 18 x 17 = 306.

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Find the equation of the line through point (-2,-2)and parallel to 3x+4y=12

Answers

Parallel = same slope
Turn 3x + 4y = 12 into y = mx + b
3x - 12 = -4y
-4y = 3x - 12
Divide by -4
Y = -3/4x + 3
Now: y = -3/4x + b
Plug in the point (-2,-2)
-2 = -3/4(-2) + b
-2 = 1.5 + b
b = -3.5
Equation: y = -3/4x -3.5
(Check my work, correct me if I’m wrong)
Here you go!! Hope this helps!


Which statement is true regarding the functions on the
graph?

f(2) = g(2)
f(0) = g(0)
f(2) = g(0)
f(0) = g(2)

Answers

Answer:

Im pretty sure its f(0) = g(0)

Step-by-step explanation:

Nina works at Sweet Smoothies. She uses 3/4 of a cup of crushed ice in each smoothie. When Nina starts her
shift, there are 24 cups of crushed ice in the ice maker. How many smoothies can she make with thatice

Answers

Answer:

32

Step-by-step explanation:

Write an equation of the line below

Answers

Answer:

I don't see the equation so when you put it I can answer

but I will help when you put the equation

Step-by-step explanation:

Put the equation to get the answer

American football is a variation of what game?
Soccer
Speedball
Field Hockey
Rugby

Answers

Answer:

Rugby

Step-by-step explanation:

They're the most similar.

Soccer you play with only your feet

Speedball you kick the ball around

Field hockey uses a stick

whats 5 1/2+2 5/6 ASAP PLEASE

Answers

Answer:

8 1/3 or 8.3 repeating

Step-by-step explanation:

you're welcome

can you answer this​

Answers

Answer:

15

Step-by-step explanation:

A chair cost $250 last year and $175 this year by what percent did the price decrease?

Answers

Answer:

I believe it is 50% decreased, not sure

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

in order to find the percentage of the price decrease,we must find the difference between the prices

250-175=75

the price has dropped 75$

to find the percentage, we do 75/250

which can be simplified to 3/10 or 30%

We can check this by finding 30% of 250 which is 75

75=75

jada mixed 8 cups of flour with 2 pints of water to make paste for an art project

Answers

Answer:

Let me check real quick

Step-by-step explanation:

simplify 3square root 5 over 4square root of 5

Answers

Answer:

5[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

This is the answer because:

1) We have to do 5^1/3 x 5^-1/4

2) Next, we do 5^1/3 - 1/4 which is 5^1/12

Therefore the answer is 5^1/12

Hope this helps!

The simplified value of the given expression is 5¹/₁₂

What is expression?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, [tex]\frac{\sqrt[3]{5} }{\sqrt[4]{5} }[/tex], we need to simplify it,

5¹/₃ / 5¹/₄

= 5⁽¹/₃-¹/₄⁾

= 5¹/₁₂

Hence, the simplified value of the given expression is 5¹/₁₂

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A 14 ft ladder is used to scale a 13 ft wall. At what angle of elevation must the laxder be situated in order to reach the top of the wall?

Answers

Answer:

The angle of elevation is equal to 68.2 degrees

Step-by-step explanation:

As you can see from the image below we are trying to find the angle on the bottom right.

We know that the hypotenuse is equal to 14 and we know that the opposite is equal to 14. This means that we will be using Sine.

sin x = 13/14

divide:

sin x = 0.9285714286

now we need to use sin^-1

sin^-1 (0.9285714286) = 68.21321071

Round 68.21321071 to the nearest tenth:

68.2

The angle of elevation is 68.2 degrees!

Answer:

[tex]\theta \approx 68^\circ[/tex]

Step-by-step explanation:

Trigonometry

The ladder, the wall, and the ground form a right triangle, where the ladder is the longest side (hypotenuse).

The trigonometric ratios stand on right triangles and can be used to relate side lengths with angles.

The angle of elevation, formed by the ladder and the ground has the height of the wall as the opposite side. Thus we can use the sine ratio, defined as:

[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]

[tex]\displaystyle \sin\theta=\frac{13}{14}[/tex]

Solving:

[tex]\displaystyle \theta=\arcsin \frac{13}{14}[/tex]

Calculating:

[tex]\mathbf{\theta \approx 68^\circ}[/tex]

3. Fiona opened a retirement account that has an annual yield of 6%. She is planning on retiring in 20 years. How much must she deposit into that account each year so that she can have a total of $600,000 by the time she retires?

Answers

pretty sure the answer will be 16,310.73 :)

Fiona must deposit  $18,277.65 into her retirement account each year for the next 20 years in order to have a total of $600,000 by the time she retires.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

The present value of an annuity is:

PV = PMT x [(1 - (1 + r)⁻ⁿ) / r]

Where PV is the present value,

PMT is the periodic payment

r is the interest rate per period (6% per year), and

n is the number of periods (20 years).

We want to find PMT, so we can rearrange the formula to solve for it:

PMT = PV x [r / (1 - (1 + r)⁻ⁿ)]

We know that PV is $600,000, r is 6% or 0.06, and n is 20.

Plugging these values into the formula, we get:

PMT = $600,000 x [0.06 / (1 - (1 + 0.06)⁻²⁰)]

PMT ≈ $18,277.65

Therefore, Fiona must deposit  $18,277.65 into her retirement account each year for the next 20 years in order to have a total of $600,000 by the time she retires.

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can you explain this question please​

Answers

Answer:

B

Step-by-step explanation:

θ and B are corresponding angles

Each is in the same position ( upper right hand corner ) in its group of four angles.

It is B
Some congruent angles are Corresponding angles. A and D are also corresponding angles.

Hope this helps! Mark me brainliest please! Cheers mate :)

Kimberly is working in the mall. He is working making $12 an hour.
She wants to buy a bicycle that costs $192. How many hours does she need to work to
have enough money ?

Answers

2,304 hope this helps youu

Solve for x.
Please.

Answers

Alive and and try it and much better

Choose the function represented by the data.
O f(x) = h2 + 4h + 80
O f(x)=5h2 -5h + 13
O f(x) = h +50h2 - 120h
O f(x) = 5h3 - 50h2 + 130h

Answers

Answer:

Option (4)

Step-by-step explanation:

To solve this problem we will satisfy the polynomials given in the options with the input-output values given in the table.

Lets take a point (4, 40),

Option (1),

f(h) = h² + 4h + 80

40 = 4² + 4(4) + 80

40 = 16 + 16 + 80

40 = 112

False.

Therefore, table doesn't represent the polynomial given in option (1).

Option (2)

f(h) = 5h²- 5h + 13

40 = 5(4)² - 5(4) + 13

40 = 80 - 20 + 13

40 = 73

False.

Therefore, table doesn't represent the polynomial given in option (2).

Option (3)

f(h) = h³ + 50h² + 13

40 = 4³ + 50(4)²+ 13

40 = 64 + 800 + 13

40 = 873

False.

Therefore, table doesn't represent the polynomial given in option (3).

Option (4)

f(h) = 5h³- 50h²+ 13h

40 = 5(4)³ - 50(4)²+ 130(4)

40 = 320 - 800 + 520

40 = 840 - 800

40 = 40

True.

Therefore, given table represents this polynomial.

Option (4) will be the answer.

if I burned 225 calories in 45 minutes how much will I burn in one minute

Answers

Answer:

5 calories per minute

Step-by-step explanation:

225÷45=5

HELP ASAP!!! determine how if possible the triangles are similar​

Answers

Answer:

d not simlar just letting u know ur getting it wrong

Step-by-step explanation:

Answer:

I think A or C would be the answer! Hope this helped a little!!

Find the GCF for the pair 4, 49. ​

Answers

i believe the GCF for the park 4 and 49 is 1.

If you were evaluating the expression (20 - 2^4)^4(20−2​4​​ )​4​​ - 6, what would you do first?

Answers

I would do the exponent first
I hope this helps you :D

Explain the meaning of the point (1,1.5) in terms of the situation.

Answers

Answer:

there will be 1.5 table spoons of olive oil for every 1 tablespoon of vineagar

Step-by-step explanation:

Find the measure of the angle which is double of its complement angle

Answers

Answer:

60°

Step-by-step explanation:

Complementary angles add to 90°, so if x is double its complement, then x + (1/2)x = 90. Doing the algebra gets you to x = 60. You know that answer is correct because 60 is double 30, which is its complement.

Find the Slope and Y Intercept of the equation of a line: y = 14x + 21.
Write your answer without using variables, decimals, or exponents.

Answers

The slope and y intercept are given
Y = mx + b
The slope is 14, the y intercept is 21

The equation of a horizontal line through (5,2) in slope-intercept form ?

Answers

Answer:

y=2 is the correct answer:)

Step-by-step explanation:

The graph of which of the following equations contains the points (2,3) and (3,2)

Answers

Answer:

[tex] y = 5 - x [/tex]

Step-by-step explanation:

The graph of the equation that will contain the points (2, 3) and (3, 2) is the graph that has a slope value that is equivalent to the slope value of the line running through the two points.

Slope of the line running through (2, 3) and (3, 2):

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 2} = \frac{-1}{1} = -1 [/tex].

Slope (m) = -1.

The equation, [tex] y = 5 - x [/tex] , is given in the slope-intercept form, which means it has a slope value of -1. I.e. the term "-x" is equivalent to -1x. So therefore, the graph of the equation that contains the points (2, 3) and (3, 2) is [tex] y = 5 - x [/tex].

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