The results of a national survey showed that on average, adults sleep 6.3 hours per night. Suppose that the standard deviation is 1.6 hours. (a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.1 and 9.5 hours. % (b) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 2.3 and 10.3 hours. % (c) Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 3.1 and 9.5 hours per day. % How does this result compare to the value that you obtained using Chebyshev's theorem in part (a)

Answers

Answer 1

Answer:

a) 75%.

b) 84%

c) Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Chebyshev Theorem:

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this question:

Mean: 6.3 hours

Standard deviation: 1.6 hours

(a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.1 and 9.5 hours.

3.1 = 6.3 - 2*1.6

9.5 = 6.3 + 2*1.6

Within 2 standard deviations, so the minimum percentage is 75%.

(b) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 2.3 and 10.3 hours.

How many standard deviations from the mean?

One standard deviation is 1.6

These measures are 10.3 = 6.3 = 6.3 - 2.3 = 4. This is k standard deviations, in which

[tex]k = \frac{4}{1.6} = 2.5[/tex]

The minimum percentage is:

[tex]100(1 - \frac{1}{k^{2}}) - 100(1 - \frac{1}{2.5^{2}}) = 84%[/tex]

So 84%.

(c) Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 3.1 and 9.5 hours per day.

Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.


Related Questions

Consider a savings account earning annual compound interest with no additional deposits or withdrawals made after the initial deposit. The balance in the account after x years can be modeled by the function s(x) = 2.000(1.045) Which statement is the best interpretation of one of the values in this function? A) The initial balance of the account is $2,000. B) The balance in the account at the end of one year is $2,000. The initial balance of the account increases at a rate of 104.5% each year. D) The initial balance of the account decreases at a rate of 4 5% each year.​

Answers

Answer:

The initial balance of the account is $2,000.

Step-by-step explanation:

I took the test on usa test prep

Answer:The initial balance of the account is $2,000.

f(x) = abx, where a = initial value, b = change factor, and x = time period.

How many notebooks do you think it would take to make a stack that is 5 feet high?​

Answers

Answer:

There are total 30 books in the 5 feet high stack of books.

Step-by-step explanation:

The complete question is

Given, Each note book is 2 inches thick, How many notebooks do you think it would take to make a stack that is 5 feet high

Solution

Thickness of each book [tex]= \frac{2}{12} = \frac{1}{6}[/tex]

The total height of the book stack is [tex]5[/tex] feet.

The number of books in the stack is equal to total height of the stack divided by the thickness of one book

Number of books in five feet high stack is

[tex]\frac{5}{\frac{1}{6} } \\5 * \frac{6}{1} \\30[/tex]

Hence, there are total 30 books in the 5 feet high stack of books.

25 divided by 12 PLEASE answer quick

Answers

24 divided by 12 equals 2,083

The division of 25 by 12  gives the quotient 2 and remainder is 1.

What is Division?

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

Given:

We have to divide 25 by 12.

The division is as follow:

                            12| 25 | 2

                                  24

                              ______

                                   1

Thus the Quotient is 2 and remainder is 1.

Learn more about Division here:

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What is the value of x in the figure above? Assume ↔B and ↔C are parallel.

Answers

Answer:

x=4

Step-by-step explanation:

180-58=26x+18

122=26x+18

122-18=26x

104=26x

4=x

write the standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point. y=a(x-h)^2+k
vertex:(4,-1) point:(2,3)

Answers

Answer:

y =  ( x − 2 ) ^ 2 + 3

y =   x^2 − 4x + 7

Step-by-step explanation:

y = a ( x − h ) ^ 2 + k

where vertex is (h,k) = (4,-1)

h=4, k=-1

y = a ( x − 4 ) ^ 2 - 1

sub ( 2,3 )

3 = a (2 - 4)^2 - 1

a=1

y = 1 ( x − 2 ) ^ 2 + 3

y =  ( x^2 − 4x + 4 )  + 3

y =   x^2 − 4x + 7

help asap i will get yelled at =( this is going to give yoyu 42 points

Answers

Answer:

24+24=48

Step-by-step

24+24=48

Answer: first pic: true. second pic: is D. third pic: false. forth pic: C.

Step-by-step explanation:

24j - 9 Factor the following expression using GCF

Answers

Answer:

See it and do it

Follow please

Please help... picture is below

Answers

Answer

x=29

Step-by-step explanation:

Okay we know that the sum of all angles in a triangle is 180, so all we have to do is add them up first

(x+17)+(2x+5)=3x+22

(3x+22)+(3x-16)=6x+6

okay so we now know that 6x+6=180

subtract 6 on both sides 6x=174

then divide by 6 to get x=29

hope this helps!

please help me with this math wuestion

Answers

Answer:

A) 3 1/4

Step-by-step explanation:

x+1/2 = 3 3/4

x = 3 3/4 - 2/4 = 3 1/4

what is the slope of (4,7) (9,7)?! please help i tried omni and it didn't give me an answer

Answers

Answer:

0

Step-by-step explanation:

The slope of a linear function is 1/5. For every rise of 5 units, what is the run?

Answers

Answer:

for every rise of 1 the run would be 25

What is the area enclosed by the curves???

Answers

the x and y axis
i think
It is 1/2 for sure , look at the photo

Let y = x² In(x).
dy/dx the lesson is differentiate products​

Answers

Answer:

dy/dx = x(1+2lnx)

Step-by-step explanation:

Given y = x² In(x).

dy/dx = Udv/dx + Vdu/dx

Let U = x², V = lnx

du/dx = 2x

dv/dx = 1/x

Substitute into the formula;

dy/dx = x²(1/x) + lnx(2x)

dy/dx = x + 2xlnx

dy/dx = x(1+2lnx)

find the area? need help guys!!​

Answers

Area = (x+6)(x+2) = x^2 + 8x + 12

a gain of five meters​

Answers

1.A gain of five meters:5

Because gain=+

Sylvester spends a total of $1725 for Common and preferred shares. He has purchased $975 worth of preferred.

Answers

Answer:

750

Step-by-step explanation:

The answer is $750.00

5 tons of compost cost $6,300.00. What is the price per pound?

Answers

Answer:

300 , is the answer

Step-by-step explanation:

A piece of land in north county is a parallelogram with a base that is four more meters than eight times the height, h. Which of the
following represents the area of the land?
A. A(n) = 8h2 + 32
B.
A(h) = 8h2 + 4
C. A(h) = 4h2 + 8h
D.
A(n) = 8h2 + 4h

Answers

Answer:

D

Step-by-step explanation:

The probability of getting a red gumball from a gumball machine is 1/8. The probability of getting a red piece of candy from a candy machine is 1/6. If both a gumball and a piece of candy are purchased, what is the probability that both are red?

Answers

Answer: 1/48

Step-by-step explanation: equation: 1/8x1/6

you have to multiply both numerators together (1x1)=1  then you multiply the denominators together (8x6)=48. you can't simplify it so your answer is 1/48

what is the following sum

Answers

Answer:

2nd option is the correct answer

[tex] 12{b}^{2} \bigg(\sqrt[3]{2a} \bigg)[/tex]

Step-by-step explanation:

[tex]3 {b}^{2} \bigg( \sqrt[3]{54a} \bigg) + 3 \bigg( \sqrt[3]{2a {b}^{6} } \bigg) \\ \\ = 3 {b}^{2} \bigg( \sqrt[3]{27 \times 2a} \bigg) + 3 \bigg( \sqrt[3]{2a {( {b}^{2} )}^{3} } \bigg) \\ \\ = 3 {b}^{2} \bigg( \sqrt[3]{ {3}^{3} \times 2a} \bigg) + 3 \bigg({\sqrt[3]{{( {b}^{2} )}^{3}2a} } \bigg) \\ \\ = 3 {b}^{2} \times 3 \sqrt[ 3]{2a} + 3 {b}^{2} \sqrt[3]{2a} \\ \\ = 9 {b}^{2} \sqrt[ 3]{2a} + 3 {b}^{2} \sqrt[3]{2a} \\ \\ = 12{b}^{2} \bigg(\sqrt[3]{2a} \bigg)[/tex]

Answer:

second option:  12b²(∛2a)

Step-by-step explanation:

you can break [tex]\sqrt[3]{54a}[/tex] into [tex]\sqrt[3]{3^3(2a)}[/tex] which equals 3[tex]\sqrt[3]{2a}[/tex]

you can break [tex]\sqrt[3]{2ab^6}[/tex] into [tex]\sqrt[3]{2ab^3b^3}[/tex] which equals b²[tex]\sqrt[3]{2a}[/tex]

now we can simplify: (3b² ·  3[tex]\sqrt[3]{2a}[/tex]) + 3b²[tex]\sqrt[3]{2a}[/tex] = 9b²[tex]\sqrt[3]{2a}[/tex] + 3b²[tex]\sqrt[3]{2a}[/tex]

this equals 12b²[tex]\sqrt[3]{2a}[/tex]

I WILL MARK BRANLIEST IF U ARE RIGHT!!

Answers

Answer:

Perimeter=100  area=688.19

Step-by-step explanation:

There's a big formula for area of pentagon and I pretty tired, so unless you want me to show my work I wont

The sector of a circle has an area of 104pi/9 square inches and a central angle with measure 65 degrees. What is the radius of the circle in inches? Show work. a. 5.7 b. 8 c. 64 d. 104

Answers

The radius of the circle is 8 inches when the sector of a circle has an area of 104pi/9 square inches.

What is a sector of a circle?

A sector is said to be a part of a circle made of the arc of the circle along with its two radii. It is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.

Which is the radius of a circle?

Radius of a circle is the distance from the center of the circle to any point on it's circumference.

Area of a sector = [tex]\frac{\theta}{360} \pi r^2[/tex]

[tex]\text{Given area = }\frac{104\times \pi}{9}=\frac{65}{360}\times \pi r^2\\\\\frac{104}{9}=\frac{65}{360} \times r^2\\\\r^2=\frac{37440}{585}\\\\r=8.001[/tex]

Hence, option b is correct, that is the radius of the circle is 8 inches.

To learn more about sector here

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The table shows the average distance in yards of the tee shots of several professional golfers and their accuracy as percentages of landing golf ball in the fairway. what does the correlation coefficient for the data indicate about the strength of the linear association between the average distance of a tee shots in the accuracy of the golf ball landing in the fairway ?

Answers

Answer: strong negative correlation

Step-by-step explanation:

Taking the test

Ben and his housemates signed a lease for an apartment for 12 months for $563 per month of which Ben agreed to pay $215 per month. Which of the following statements best gives the reasons that Ben’s rent payment is an essential (fixed) expense?

Answers

Answer:

It is by contract the same amount every month.

Step-by-step explanation:

Find the factors of following:
(i) 8x^2 yy

Answers

Answer:

i•8xy^2yz

Step-by-step explanation:

Remove unnecessary parentheses

Answer:

i) 8x^2 yz=2×2×2×x×x×y×z

The arrow shown is on a sign. What is the area of the arrow? Plz

Answers

Answer:

61 inches squared

Step-by-step explanation:

find the area of the rectangle then the area of the triangle and add.

Answer:

61 in²

Step-by-step explanation:

first u work out the rectangle. so u do 4 times 10 which is 40 . then u do 1.5 plus 1.5 plus 4 which equals 7 . then u do 7 times 6 which is 42 . 42 two divide by 2 = 21 . 21 plus 40 equals 61. answer 61.

area of triangle: base times height divide by 2 .

to work out area of rectangle : 4×10=40 in²

1.5+1.5+4= 7 in

area of triangle: 7×6=42 then divide by 2 = 21 in²

plus them to get the area of arrow : 21+40=61 in²

hope this helps. give brainliest and like this . rate it and follow me . amd I will follow u back and help u more

Could someone help me with this

Answers

Answer:

try to do this formula

XYZ

= X times Y times Z

Wright et al. [A-2] used the 1999-2000 National Health and Nutrition Examination Survey(NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium (mg). They found in all adults 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454. Using these values for the mean and standard deviation for the U.S. population, find and interpret the probability that a random sample of size 50 will a mean:

Answers

Complete question :

Wright et al. [A-2] used the 1999-2000 National Health and Nutrition Examination Survey NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium in all adults 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454. Usin these values for the mean and standard deviation for the U.S. population, find the probability that a randonm sample of size 50 will have a mean: (mg). They found a) Greater than 800 mg b) Less than 700 mg. c) Between 700 and 850 mg.

Answer:

0.10935

0.3718

0.9778

0.606

Step-by-step explanation:

μ = 721 ; σ = 454 ; n = 50

P(x > 800)

Zscore = (x - μ) / σ/sqrt(n)

P(x > 800) = (800 - 721) ÷ 454/sqrt(50)

P(x > 800) = 79 / 64.205295

P(x > 800) = 1.23

P(Z > 1.23) = 0.10935

2.)

Less than 700

P(x < 700) = (700 - 721) ÷ 454/sqrt(50)

P(x < 700) = - 21/ 64.205295

P(x < 700) = - 0.327

P(Z < - 0.327) = 0.3718

Between 700 and 850

P(x < 850) = (850 - 721) ÷ 454/sqrt(50)

P(x < 850) = 129/ 64.205295

P(x < 700) = 2.01

P(Z < 2.01) = 0.9778

P(x < 850) - P(x < 700) =

P(Z < 2.01) - P(Z < - 0.327)

0.9778 - 0.3718

= 0.606

If f (x) = x – 1 and g(x) = 5x – 2 , then (f/g) (x) help me plz

Answers

Answer:

[tex](f/g)x = \frac{x-1}{5x - 2}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x - 1[/tex]

[tex]g(x) = 5x - 2[/tex]

Required

(f/g)x

In functions:

[tex](f/g)x = \frac{f(x)}{g(x)}\ \ \ g(x)\ne 0[/tex]

So:

[tex](f/g)x = \frac{x - 1}{5x - 2}[/tex]

Help pls!! I need help!!

Answers

Answer:

what u need help wt?

Step-by-step explanation:

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