Anna's project for her introductory statistics course was to compare the selling prices of textbooks at two Internet bookstores. She first took a random sample of ten textbooks used that term in courses at her​ college, based on the list of texts compiled by the college bookstore. Then, she obtained prices of the 10 randomly selected textbooks at the two Internet sites to test if the average prices of textbooks sold at the two internet bookstores are different. The prices of those textbooks at the two Internet sites are shown below. Perform a significance test comparing the population mean prices.
Site A $115 $79 $42 $138 $96 $25 $81 $97 $117 $69
Site B $110 $79 $39 $129 $96 $2 569 $97 $107 $66 5
Let mu_d be the population mean difference in price. State the hypotheses to test whether there is a difference in the mean price between the two Internet bookstores. Choose the correct answer below.
A. H_0: mu_d notequalto 0 and H_a: mu_d = 0
B. H_0: mu_d = 0 and H_3: mu_d > 0
C. H_0: mu_d = 0 = 0 and H_a: mu_d notequalto 0
D. H_0: mu_d = 0 and H_a: mu_d < 0
1. Determine the test statistic t = ______(Round to three decimal places as needed.)
2. Determine the P-value. P-value = _______(Round to three decimal places as needed.)

Answer:

|Z| = |-0.126| = 0.126 < 1.645

Null hypothesis is accepted

The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.

μ = 57.5

Step-by-step explanation:

Explanation:-

The average retirement age for a certain country was reported to be 56.4 years

The mean of the sample x⁻ = 56.4

The standard  deviation of the Population 'σ'= 55 years

The mean of the population μ = 57.5

Null hypothesis: H₀:The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.

μ = 57.5

Alternative Hypothesis : H₁: μ ≠57.5

Test statistic

         [tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

critical value:

[tex]Z_{\frac{\alpha }{2} } = Z_{0.05} =1.645[/tex]

[tex]Z = \frac{56.4-57.5 }{\frac{55}{\sqrt{40} } } = -0.126[/tex]

|Z| = |-0.126| = 0.126 < 1.645

The null hypothesis is accepted

Conclusion:-

The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.

μ = 57.5

Answer:

[tex]9^2-x^2[/tex] and [tex]x(9-x)+9(9-x)[/tex]

Step-by-step explanation:

The area of the larger square is 9*9=9^2. The area of the smaller square inside of it is x*x=x^2. The area of the light shaded gray is therefore 9^2-x^2, which is also equivalent to x(9-x)+9(9-x). Hope this helps!

Answer:

  65,280

Step-by-step explanation:

Consider the 4×4 grid ...

  [tex]\left[\begin{array}{cc}a&b\\d&c\end{array}\right][/tex]

where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.

The same will be true of 270° rotational symmetry, for the same reason.

__

For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)

__

The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...

  65,536 -256 = 65,280 . . . . colorings not rotationally symmetric

You can use the divergence theorem:

[tex]\vec v=z\,\vec\imath+y^2\,\vec\jmath+x^2\,\vec k[/tex]

has divergence

[tex]\mathrm{div}\vec v=\dfrac{\partial z}{\partial x}+\dfrac{\partial y^2}{\partial y}+\dfrac{\partial x^2}{\partial z}=2y[/tex]

Then the rate of flow out of the cylinder (call it R) is

[tex]\displaystyle\iint_{\partial R}\vec v\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec v\,\mathrm dV[/tex]

(by divergence theorem)

[tex]=\displaystyle2\int_0^{2\pi}\int_0^5\int_0^1r^2\sin\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]

(after converting to cylindrical coordinates)

whose value is 0.

Answer:

SA = 1,176 ft².

Step-by-step explanation:

To find the surface area of the triangular prism, we can solve for the rectangular base, both triangular faces, and lateral sides separately.

For the rectangular base: (Use formula l×w)

20 × 18 = 360 ft²

For the triangular faces: (Use formula 1/2(b·h)

1/2(18 × 12) = 108 ft²

Since there are two faces, we need to double the amount.

108 × 2 = 216 ft².

Finally, solve for the lateral sides:

20 × 15 = 300 ft².

There are two sides, so:

300 × 2 = 600 ft².

Add up all of these areas:

600 + 216 + 360 = 1,176 ft²

Answer:

-20

Step-by-step explanation:

the inverse of the equation (flipping all the signs except for the equal sign) would be 44-24=20. So flip the signs back and you get -44 + 24 = -20

Answer:

(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.

(b) Two samples are described in the above situation, that is;

(c) The average age of 37 years is a statistic.

(d) The above information represents a quantitative variable.

(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.

Step-by-step explanation:

We are given that a research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years.

When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years.

(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.

(b) Two samples are described in the above situation, that is;

(c) The average age of 37 years is a statistic as it is the sample average age of visitors to the park on a weekday, i.e. [tex]\bar X_1[/tex] = 37 years.

(d) The above information represents a quantitative variable because in this we are concerned about the average age of visitors in the park which is a numeric value and we are not interested in any qualitative aspect.

(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.

But during weekends like Saturday, the schools or coaching institutions are generally closed due to which they are able to come to parks to play and because of this there are large number of children below 20 years of age who visit parks on weekends.

Answer:

Necesita cubrir 4800 cm^2.

Step-by-step explanation:

La pregunta está incompleta:

Laura quiere cubrir con papel de china una puerta como la que se muestra en el dibujo. Las medidas son 80 cm de largo y 60 cm de ancho.

Tenemos que calcular la superficie de la puerta, cuyas medidas son 80 cm de largo y 60 cm de ancho.

Para calcular el área simplemente multiplicamos las medidas de ambos lados:

[tex]A=80\,cm\cdot 60\,cm=4800\,cm^2[/tex]

Answer: Choice B. 54degrees

Step-by-step explanation:

Angles 1 4 5 8 are equal and angles 2 3 6 7 are also equal. These two sets of angles of supplementary(you‘d get 180 by adding them).

so

13x+9=180-(5x+9)

by simplifying the equation youll get

18x+18=180

x=9

so angle 7(and therefore angle 6) equals

5*9+9=54

Answer:

[tex]P(19<X<91)=P(\frac{19-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{91-\mu}{\sigma})=P(\frac{19-55}{12}<Z<\frac{91-55}{12})=P(-3<z<2)[/tex]

And we can find this probability with this difference and using the normal standard distribution

[tex]P(-3<z<3)=P(z<3)-P(z<-3)=0.9987 -0.00135 =0.9974[/tex]

Step-by-step explanation:

Let X the random variable that represent the amount of Jen monthly phone of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(55,12)[/tex]  

Where [tex]\mu=55[/tex] and [tex]\sigma=12[/tex]

We are interested on this probability

[tex]P(19<X<91)[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Replacing the info we got:

[tex]P(19<X<91)=P(\frac{19-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{91-\mu}{\sigma})=P(\frac{19-55}{12}<Z<\frac{91-55}{12})=P(-3<z<2)[/tex]

And we can find this probability with this difference and using the normal standard distribution

[tex]P(-3<z<3)=P(z<3)-P(z<-3)=0.9987 -0.00135 =0.9974[/tex]

Answer:

Quadrilateral ABCD is a Quadrilateral with four equal sides so either a rhombus or square

But

Quadrilateral ABC'D is a quadrilateral with two adjacent sides equal so it's a kite shape

Step-by-step explanation:

(11, -7), B(9, -4), C(11, -1), and D(13, -4).

Let's take out the values of x and y coordinate with the way they are arranged

X = 11,9,11,13

Y = -7,-4,-1,-4

So we observe that distance of the coordinates on either x is 2 units and y is 3 units.

But when the the value was changed to

C′(11, 1), (11, -7), B(9, -4), C′(11, 1), and D(13, -4).

There was difference of 2 unit and 4 unit making the new shape a kite.

The diagram attached explain better

Answer:

1. rhombus with non-perpendicular adjacent sides

2. kite

Step-by-step explanation:

i just got it right on edmentum.

Please mark as brainliest.

Answer: y=1/2x-1

Step-by-step explanation:

To find the equation of the line that passes through the points, we need to find out slope, m.

[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

We plug our points into this formula to find slope.

[tex]m=\frac{1-2}{4-6} =\frac{-1}{-2} =\frac{1}{2}[/tex]

Our slope is 1/2. To find our y-intercept, b, we would plug any point into the equation for slope-intercept form.

y=mx+b

y=1/2x+b

1=1/2(4)+b

1=2+b

b=-1

Now that we know b, our equation is y=1/2x-1.

Answer:

Length of the given arc AB = 7.33 in.

Step-by-step explanation:

Formula to calculate the arc length is,

Arc length = [tex]\frac{\theta}{360}(2\pi r)[/tex]

Where θ is the measure of central angle subtended by the arc.

And 'r' = radius of the circle

By substituting the values given in the formula,

Length of arc AB = [tex]\frac{60}{360}\times (2\pi )\times (7)[/tex]

                            = [tex]\frac{14\pi}{6}[/tex]

                            = [tex]\frac{7\pi}{3}[/tex]

                            = 7.33 in.

Therefore, length of the given arc AB = 7.33 in.

The question is incomplete, I will however explain, with an illustration, how to determine the center and radius of a circle.

Step-by-step explanation:

The standard equation of a circle is given as:

(x - a)² + (y - b)² = r² ........................(1)

Where (a, b) is the center of the circle, and r is the radius.

An expression can be given for us to find the center and the radius of the circle.

Suppose we were given the expression:

x² + y² - 10x + 4y - 7 = 0.....................(2)

To find the center and the radius, it is left for us to rewrite (2) in the form of (1).

Rearranging (2), we have

(x² - 10x) + (y² + 4y) = 7

Completing the squares of each bracket

(x² - 10x + 25 - 25) + (y² + 4y + 4 - 4) = 7

(x² - 10x + 25) + (y² + 4y + 4) - 25 - 4 = 7

(x² - 10x + 25) + (y² + 4y + 4) - 29 = 7

(x - 5)² + (y + 2)² = 7 + 29

(x - 5)² + (y + 2)² = 36

Or

(x - 5)² + (y + 2)² = 6² .....................(3)

Comparing (3) with one, we see that

a = 5, b = -2, and r = 6

Therefore it is a circle centered at (5, -2) with a 6 unit radius.

Answer:

[tex] 0.34 \leq p \leq 0.38[/tex]

For this case we can conclude that with 98% of confidence the true proportion of Drosophila in a population would be between 0.34 and 0.38.

But that doesn't means that we have 98% of PROBABILITY that the true proportion would be between 0.34 and 0.38, because we are constructing a confidence interval with sample data and we can't analyze this using probability.

Then the best answer is:

2. False

Step-by-step explanation:

For this case we have a confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be given by:

[tex] 0.34 \leq p \leq 0.38[/tex]

For this case we can conclude that with 98% of confidence the true proportion of Drosophila in a population would be between 0.34 and 0.38.

But that doesn't means that we have 98% of PROBABILITY that the true proportion would be between 0.34 and 0.38, because we are constructing a confidence interval with sample data and we can't analyze this using probability.

Then the best answer is:

2. False

Answer:

SEND MONEY

Step-by-step explanation:

A cypher shift encrypts a message by shifting each letter a certain number of places.

For example, N is the 14th letter of the alphabet.

If we shift 9 places to the left, we get the 5th letter of the alphabet, which is E.

Or, if we shift 9 places to the right, we get the 23rd letter of the alphabet, which is W.

Assuming the shift is to the left:

B = 2

2 − 9 = -7

-7 + 26 = 19

19 = S

N = 14

14 − 9 = 5

5 = E

W = 23

23 − 9 = 14

14 = N

M = 13

13 − 9 = 4

4 = D

V = 22

22 − 9 = 13

13 = M

X = 24

24 − 9 = 15

15 = O

W = N

N = E

H = 8

8 − 9 = -1

-1 + 26 = 25

25 = Y

SEN DMO NEY

SEND MONEY

Answer:

10.71

Step-by-step explanation:

The arc length is

2*3*3.14/4 = 4.71

Add to the two side lengths to get the perimeter

4.71+3+3 = 10.71

[tex]answer = 10.71 \: millimeters \\ solution \\ radius = 3 \: millimeters \\ perimeter \: of \:quarter \: circle \\ = \frac{2\pi \: r}{4} + 2r \\ = \frac{2 \times 3.14 \times 3}{4} + 2 \times 3\\ = \frac{18.84}{4} + 6 \\ = \frac{18.84 + 6 \times 4}{4} \\ = \frac{18.84 + 24}{4} \\ = \frac{42.84}{4} \\ = 10.71 \: millimeters \\ hope \: it \: helps[/tex]

Answer:

c) Permutations: 40320

Step-by-step explanation:

We have that permutations are groupings in which the order of the objects matters. Combinations are groupings where content matters but order does not.

In this case, then the batting order, therefore the order does matter, therefore, it would be a permutation, where n = 8 and r = 7

nPr = n! / (n-r)!

Replacing:

8P7 = 8! / (8-7)! = 40320

Which means that the answer is c) Permutations: 40320

Answer:

isn't X=21 because it's a right angle and you just do 90-69=21?

Answer:

alpha = 21°

Step-by-step explanation:

You see that this rectangle has four right angles, meaning each of 90 °

That is why it is called a rectangle in the first place. ( The 'rec' in rectangle stands for 'right' or 'streight' and it indicates all angles in the rectangle being 90 °).

Anyway, corner alpha added with the given angle of 69 ° must there fore add up to the value of a streight corner, right?

apha + 69 = 90

alpha = 90 - 69

alpha = 21°

Answer:

Option A Ordinal

Step-by-step explanation:

The most appropriate level of measurements for this category is ordinal measurements. The ordinal measurement allows for the ordering of the data but differences cannot be found for them or finding differences is completely useless using this measurements.

Answer:

Dear Laura Ramirez

Answer to your query is provided below

The ratio of triangle XYZ is 1:√3 :2.

Step-by-step explanation:

A 30-60-90 right triangle (literally pronounced "thirty sixty ninety") is a special type of right triangle where the three angles measure 30 degrees, 60 degrees, and 90 degrees. The triangle is significant because the sides exist in an easy-to-remember ratio: 1:√3 :2.

Answer:

Answer is A $172.25

Step-by-step explanation:

Step 1: Our output value is 575.50.

Step 2: We represent the unknown value with $x$.

Step 3: From step 1 above,$575.50=100\%$.

Step 4: Similarly, $x=30\%$.

Step 5: This results in a pair of simple equations

$575.50=100\%(1)$.

$x=30\%(2)$.

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

$\frac{575.50}{x}=\frac{100\%}{30\%}$

Step 7: Again, the reciprocal of both sides gives

$\frac{x}{575.50}=\frac{30}{100}$

$\Rightarrow x=172.65$

Therefore, $30\%$ of $575.50$ is $172.65$

Answer:

The total that will be saved at a 30% discount is $172.65

Explanation:

Since, the marked up price of the item will be $575.50,

and the discount percentage is 30%,

Therefore, $ 172.65 will be saved.

Answer:

The advertising cost, X₄ = 5.626 million

The 80% confidence limits for X₄ is (5.041 , 6.100)

The 80% prediction limits for X₄ is (4.048 , 7.094)

Step-by-step explanation:

Using MINITAB

The regression equation is X₄ = 4.14 + 0.0431 X₁ - 0.800 X₂ + 0.00059 X₃ - 0.661 X₅ + 0.057 X₆

Predictor Coef SE Coef T P

Constant 4.142 1.626 2.55 0.019

X₁ 0.043089 0.009466 4.55 0.000

X₂ -0.7998 0.2515 -3.18 0.005

X₃ 0.000590 0.004221 0.14 0.890

X₅ -0.6606 0.1542 -4.28 0.000

X₆ 0.0574 0.1254 0.46 0.652

S = 1.07911 R-Sq = 93.4% R-Sq(adj) = 91.8%

Analysis of Variance

Source DF SS MS F P

Regression 5 345.966 69.193 59.42 0.000

Residual Error 21 24.454 1.164

Total 26 370.420

Source DF Seq SS

X₁ 1 309.464

X₂ 1 8.699

X₃ 1 5.994

X₅ 1 21.566

X₆ 1 0.244

Unusual Observation

Obs X₁ X₄ Fit SE Fit Residual St Resid

17 398 5.500 7.714 0.641 -2.214 -2.55 R

27 400 7.000 7.366 1.025 -0.336 -1.00 X

Where R is observation with a large standardized residual.

Where X is observation whose X values give it large influence.

Predicted values for new Observations

New

Obs Fit SE Fit 80% Cl 80% Pl

1 5.571 0.400 (5.041 , 6.100) (4.048 , 7.094)

Values of Predictors for New Observations

New

Obs X₁ X₂ X₃ X₅ X₆

1 163 2.40 188 6.60 10.0

∴ The advertising cost, X₄ = 5.626 million, The 80% confidence limits for X₄ is (5.041 , 6.100), and The 80% prediction limits for X₄ is (4.048 , 7.094)

Answer:

B. FOIL

Step-by-step explanation:

FOIL stands for Firsts, Outsides, Insides, and Lasts

This is a mnemonic to help you to remember how to multiply two binomials

From the image, we can see that the on the right side of the equals,

[tex](x)(-5x^2)[/tex] is the product of the firsts of the binomials

[tex](x)(x)[/tex] is the product of the outsides of the binomials

[tex](-2)(-5x^2)[/tex] is the product of the insides of the binomials

[tex](-2)(x)[/tex] is the product of the lasts of the binomials.

Answer:

  B.  FOIL

Step-by-step explanation:

"FOIL" is an acronym for First, Outer, Inner, Last. It refers to the relative positions of the terms in the multiplication of binomials.

The given equation shows the result of such a multiplication. It is an example of the application of FOIL.

Answer:

Red apples to all apples =2/11

Red apples to green apples =2/9

Step-by-step explanation:

There are 11 total apples 9 of them are green and the rest are red so there are 11-9=2 red apples

The ratio of red apples to all apples = number of red apples ÷ total apples number = 2÷11

The ratio of red apples to green apples = number of red apples ÷ number of green apples = 2÷9

Answer:

Red apples to all apples =2/11

Red apples to green apples =2/9

Step-by-step explanation:

There are 11 total apples 9 of them are green and the rest are red so there are 11-9=2 red apples

The ratio of red apples to all apples = number of red apples ÷ total apples number = 2÷11

The ratio of red apples to green apples = number of red apples ÷ number of green apples = 2÷9

Step-by-step explanation:

Answer:

There is insufficient statistical evidence to prove that the companies stated color distribution is not correct therefore, the overall proportions of the colors are correctly stated as above

Step-by-step explanation:

We have that

H₀: 0.24 blue, 0.13 brown, 0.20 green, 0.16 orange, 0.13 red and 0.14 yellow

The Data given are as follows;

Hₐ: The stated distribution of M&M is incorrect

                        Blue   Brown   Green    Orange   Red    Yellow   Total

Observed:        105     72          89          84           70       80          500

Expected:         120     65         100         80           65       70      

We have;

[tex]\chi ^{2}=\dfrac{\left (105-120 \right )^{2}}{120}+ \dfrac{\left (72-65\right )^{2}}{65} + \dfrac{\left (89-100\right )^{2}}{100} + \dfrac{\left (84-80\right )^{2}}{80} + \dfrac{\left (70-65\right )^{2}}{65} + \dfrac{\left (80-70\right )^{2}}{70} = 5.85[/tex]

At 6 - 1 = 5 degrees of freedom we find the p-value from the chi squared table as follows

P(0.05) at 5% degrees of freedom =11.070 hence our P-value is larger than 0.05 and we fail to reject the null hypothesis, hence there is insufficient statistical evidence to prove that the companies stated color distribution is not correct.

Answer:

1 the person can get heads because if the coin flips and spins and the coin stop the person is most likey to get heads 2 the person can just flip the coin and pray he/she get heads

Step-by-step explanation:

hope this helps you :)

Answer:

Step-by-step explanation:

Hello!

The variable of interest is "the time a fight lasts" measured in seconds

The five number summary for her first 12 UFC fights are:

Minimum: Min= 14

First Quartile: Q₁= 25

Second Quartile/Median: Me= 44

Third Quartile: Q₃= 64

Maximum: Max= 289

a)

Three of her fights lasted more than one minute: 289, 267, 66. Out of these three fights, you have to determine if they are outliers using the IQR method.

The IQR is the distance between the third quartile and the first quartile

IQR= Q₃ - Q₁= 64 - 25= 39

Remember, an outlier is an observation that is significantly distant from the rest of the data set. They usually represent experimental errors (such as a measurement) or atypical observations. Some statistical measurements, such as the sample mean, are severely affected by this type of values and their presence tends to cause misleading results on a statistical analysis.  

Considering the 1st quartile (Q₁), the 3rd quartile (Q₃) and the interquartile range IQR, any value X is considered an outlier if:

X < Q₁ - 1.5 IQR

X > Q₃ + 1.5 IQR

Or extreme outliers if:

X < Q₁ - 3 IQR

X > Q₃ + 3 IQR

The limits that define if a value is an outlier or not are:

X < 25 - 1.5*39 = -33.5

X > 64 + 1.5*39= 122.5

And for extreme outliers:

X < 25 - 3*39 = -92

X > 64 + 3*39= 181

So fights that lasted less than -33.5 or more than 122.5 seconds are to be considered outliers, and those who lasted less than -92 or more than 181 seconds are extreme outliers.

Out of the three fights, the ones that lasted 289 and 267 seconds can be considered extreme values.

b) The minimum observed value for this data set is 14 seconds, values are considered to be outliers if they are less to -33.5, so there is no low outliers on the sample.

As you can see, both values that allow you to determine if the observation is an outlier or not are negative, since the variable is "the time a fight lasts" it is impossible for it to have negative values. The lowest value of time a fight can last is "zero seconds". Although mathematically correct, these values make no sense.

c)

See attachment.

d)

The average or mean is a measurement of central tendency that shows you the value around which most of the distribution will be. It is very affected by the presence of outliers, especially extreme ones. Outliers make the mean "move" towards them, this means, that if there are small outliers, then the mean will move to the lower side of the distribution. But if the outliers are big, then the mean will move to the higher side of the distribution.

For example, let's say 5 of the fight times were:

10, 37, 49, 51, 68

For these values the mean would be:

X[bar]₀= ∑X/n= (10+37+49+51+68)/5= 215/5= 43

Now let's change one of these values for an extreme one:

Small value:

0, 37, 49, 51, 68

X[bar]₁= ∑X/n= (0+37+49+51+68)/5= 205/5= 41

⇒ As you can see, one change for a smaller value reduces the mean value X[bar]₁ < X[bar]₀

Big value:

10, 37, 49, 51, 268

X[bar]₂= ∑X/n= (10+37+49+51+268)/5= 415/5= 83

⇒ In this case, changing one of the 5 values to a bigger one moved the mean to the right: X[bar]₀ < X[bar]₂

So for the given distribution, since there are at least two high outliers, you'd expect the mean to be greater than the median.

I hope this helps!

Answer:

Now we have everything in order to replace into formula (1):

[tex]18-2.262\frac{2.75}{\sqrt{10}}=16.03[/tex]    

[tex]18+2.262\frac{2.75}{\sqrt{10}}=19.97[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X=18[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=2.75 represent the sample standard deviation

n=10 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]

The Confidence is 0.90 or 90%, the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical vaue would be [tex]t_{\alpha/2}=2.262[/tex]

Now we have everything in order to replace into formula (1):

[tex]18-2.262\frac{2.75}{\sqrt{10}}=16.03[/tex]    

[tex]18+2.262\frac{2.75}{\sqrt{10}}=19.97[/tex]    

Answer:

72.

Step-by-step explanation:

Given a group of 6, 9 and 12.

We are to determine the least number of patties that will be shared equally among the groups.

This we do by determine the Least common multiple of the three numbers.

[tex]6=2 X 3\\9 = 3 X 3\\12 =2 X 2 X 2\\L.C.M.=2^3X3^2=72[/tex]

Therefore, the least number of patties that can be shares equally among groups of 6, 9 and 12 is 72.