"if we have a distribution of x values that is more or less mound-shaped and somewhat symmetrical, what is the sample size n needed to claim that the distribution of sample means x from random samples of that size is approximately normal"

Answers

Answer 1

Answer: 30 or greater.

Explanation:
The Central Limit Theorem (CLT) states that the distribution of sample means is normally distributed.

If the distribution is already known to be Gaussian, then smaller sample sizes than 30 will be fine to use.

If the distribution is not known, then a minimum sample size of 30 is needed to guarantee that the CLT holds.

Typically,
[tex]\bar{x} = \mu \\ s = \frac{\sigma}{ \sqrt{n} } [/tex]
where
[tex]\bar{x}[/tex] = sample average
μ = population mean
s = sample standard deviation
σ = population standard deviation
n = sample size

Related Questions

calculate the length of the hypotenuse

Answers

hypotenuse =sqrt( a^ + b^

10^2 = 100

14^2 = 196

196+100 = 296

sqrt(296) = 17.20

Answer is D. 17.20

4000 is 1/10 as much as what number

Answers

40,000

All you do is multiply 4,000 by 10 to find out what 10 times of your number is, if 4,000 is only 1/10 of it.

To find a number that is 1/10 as much as 4000, you would multiply 4000 by 10, resulting in 40000.

To find the number that is 1/10 of 4000, you need to divide 4000 by 1/10, which is the same as multiplying by its reciprocal, 10.

Step 1: Write down the expression:

Let ( x ) be the number we're looking for.

Step 2: Set up the equation:

[tex]\[ x = \frac{4000}{\frac{1}{10}} \][/tex]

Step 3: Multiply by the reciprocal:

x = 4000 \times 10

Step 4: Solve:

x = 40000

So, the number that is 1/10 as much as 4000 is 40000.

Ricky is taking out a personal loan for $12,000 to remodel his kitchen. He would like the lowest monthly payment possible, even if it means a bigger finance charge in the end. His bank has offered him a loan at 13% interest for 36 months or 12% interest for 60 months, both of which are compounded monthly. Which of the following statements most accurately describes what Ricky should be thinking? a. More payments with the 60 month loan will give him the lowest monthly payment. b. Fewer payments with the 36 month loan will give him the lowest monthly payment. c. The 60 month loan comes with a bigger finance charge and, thus, a bigger monthly payment. d. The 36 month loan comes with a bigger finance charge and, thus, a bigger monthly payment.

Answers

Answer : The correct Option is A.

Step-by-step Explanation :

To solve this we are going to use the monthly payment formula:

[tex]\text{Payment = }\frac{Rate\times Principal}{1-(1+Rate)^{-n}}}[/tex]

where, Principal is the amount of the loan

n is the number of periods.

Option A. 13% interest for 36 months compounded monthly

Ricky is taking out a personal loan for $12,000 and term of the loan is 36 months ⇒ n = 36. To find the rate per period, we first need to convert the interest rate to decimal form ⇒ Rate = 0.13.

Now since the bank is charging him the interest rate for the 36 months, we just need to divide the interest rate (in decimal form) by the number of months (36) to find the rate per period

[tex]\implies\text{Rate per period = }\frac{0.13}{36}[/tex]

So, putting all these values in the formula, We get monthly payment of loan A = $356.07

Option B : 12% interest for 60 months compounded monthly

interest rate in decimal form = 0.12

By replacing the values in formula the monthly payment of loan B is $212.44

Option C and Option D are obviously denied as the financial charge is not effected by the monthly payments so ricky will not be thinking about the financial charge.

Now, Monthly payments of loan B are significantly low than that of monthly payments of loan A.

So, we can conclude that the correct answer is a. More payments with the 60 month loan will give him the lowest monthly payment.

Answer:

Step-by-step explanation:

Solve the following system by the substitution method. Check the solution(s). 0.1x+0.2y=-0.6 and 0.6x-0.3y=2.3

Answers

(1.8666666,-3.9333333)

sally has scores of 88, 92, 80, and 96. find the score she must make on the next exam to have an average of 90

Answers

The score range that sally would have to make a 90 average is 85-100

A 180 day $3 million negotiable cd has a 4.25% annual rate quote. if you buy the cd, how much will you collect in 180 days?

Answers

$3 mill×[1 + (0.0425×180/360)

Round 527 to the nearest hundred

Answers

500 because the 2 in the tens spot is less than five so therefore you keep the 5 in the hundreds spot the same

Solve the equation.

3(k−6) = 15

k = ____?

Answers

Distribute
3k-18=15
Get k by itself, add 18 to both sides
3k=33
Divide by 3 to both sides to make k by itself
k=11

this is the answer..........

thw ration of two elements prontons is equivalent to 3 to 1. What are those two elements? A) gold to tin B)nein to tin C) platinum to iron D) silver to gold

Answers

[tex]\bf a)\qquad \cfrac{gold}{tin}\implies \cfrac{79}{50}\impliedby \textit{no dice} \\\\\\ b)\qquad \cfrac{neon}{tin}\implies \cfrac{10}{50}\implies \cfrac{1}{5}\impliedby \textit{no dice} \\\\\\ d)\qquad \cfrac{silver}{gold}\implies \cfrac{47}{79}\impliedby \textit{nope, no dice either}[/tex]

At the beginning of a bake sale mary set aside 4 pies for herself karen bought half of the remaining pies for her birthday party and 5 more pies were sold during the sale. When the sale was over there were 19 pies remaining. How msny pies were there before the bake sale started

Answers

There were fifty two pies at the start of the bakesale. If you work backwards, the original number of pies was subtracted by four, divided by two, and then subtracted by five. If you started with nineteen and then undid all of that, you get 52

There were 52 pies before the bake sale started as per the provided condition.

Let's break down the information given step by step:

At the beginning of the bake sale, Mary set aside 4 pies for herself. So, the number of remaining pies is the total number of pies minus 4.

Karen then bought half of the remaining pies for her birthday party. This means the number of remaining pies is now half of the previous remaining pies.

Next, 5 more pies were sold during the sale. Therefore, the number of remaining pies is further reduced by 5.

Finally, when the sale was over, there were 19 pies remaining.

Let's use variables to solve the problem. Let's say the initial number of pies before the sale started is "x."

After Mary set aside 4 pies, the number of remaining pies is (x - 4).

Karen bought half of the remaining pies, so the number of remaining pies becomes (x - 4)/2.

5 more pies were sold, reducing the number of remaining pies to (x - 4)/2 - 5.

According to the given information, (x - 4)/2 - 5 equals 19.

Now, we can solve the equation to find the value of x:

(x - 4)/2 - 5 = 19

Simplifying the equation, we have:

(x - 4)/2 = 24

(x - 4) = 48

x = 52

Therefore, there were 52 pies before the bake sale started.

To learn more about the equation;

https://brainly.com/question/12788590

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Pamela wants to buy a suitcase whose dimensions are 1 1/2 times those of her 28 times 16 times 8 inch suitcase. How is the ratio of the volumes related to the ratio of corresponding dimensions? What is the ratio of the volumes?

Answers

ok

volume=length times width times height
her current suitcase volume is 28*16*8=3584 cubic inches

her new one will have each dimention mulipled by 1 and 1/2 or 1.5

so
newV=(1.5*28)*(1.5*16)*(1.5*8)
newV=12096 cubic inches

ratio is 12096/3584=3.375=1.5*1.5*1.5

the ratio is new:old=3.375:1

Thus the required ratio is 3.375

Pamela wants to buy a suitcase whose dimensions are 1 1/2 times of her 28 times 16 times 8 inch suitcase.
What is the ratio of the volumes?

What is the Ratio?

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

volume of former suitcase = 28 x 16 x 8

=3584 cubic inches

volume of latter suitcase
=1.5x28 x1.5x16 x1.5x8
=12096
ratio of volumes
= 12096/3584
=3.375

Thus the required ratio is 3.375 of volumes of suitcase.

Learn more about Ratio here:

brainly.com/question/13419413

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What scale of measurement is being used when a teacher measures the number of correct answers out of 50 on a quiz for each student?

Answers

AssessmentA broad term used to describe a systematic process used to collect information.TestA systematic procedure for measuring a sample of behavior from a domain.MeasurementThe process of assigning numbers to some characteristic according to some specified rules.Item Difficulty for a test item scored incorrect (0) or correct (1) from a classical test theory perspectiveProportion of individuals out of the total number of individuals who answered the item correctly (40 students out of 100 answered the item correctly = .40; the bigger the number the "easier" the item).Item Discrimination for a test item scored incorrect (0) or correct (1) from a classical test theory perspectiveDegree to which an item differentiates people who score high on the total test from those who score low on the total test. Item-total correlation is one way of defining item discrimination. You want items to have positive values for item discrimination.Item Variance for a test item scored incorrect (0) or correct (1) from a classical test theory perspectiveItem variance = (proportion of individuals who answered the item correctly) x (proportion of individuals who answered the item incorrectly)
p x qCovariance between 2 variablesCovariance is a measure of the linear association between 2 variables with the 2 variables represented in their original units (not standardized). Unlike a correlation coefficient that goes from -1 to +1, the value of a covariance can go from - infinity to + infinity.Pearson product moment correlation (r) between 2 variablesPearson correlation (r) is a measure of the linear association between 2 variables with the 2 variables being standardized (mean = 0, SD = 1). Correlation coefficient that goes from -1 to +1Variance-Covariance MatrixIn a variance-covariance matrix the variances of the variables are represented in the diagonal of the matrix; the covariances between pairs of variables are represented in the off diagonalConstructAn unobserved or latent variable that is used to explain some observed phenomenon or experience. Latent variables are represented by a circle in measurement models.Reflective Measurement ModelA measurement model that holds that holds that a construct is viewed as the cause of the observed or measured variables.Formative Measurement ModelA measurement model that holds that holds that the observed or measured variables are the cause of the latent variableOperational Definition of a ConstructA definition that is clear and detailed that defines the construct by specifying the procedures used to measure a constructContent ValidityOne of five sources of measurement validity evidence that often involves experts who are knowledgeable about the construct making evaluative judgments about whether the items used to measure the construct adequately reflect the definition of the construct.Convergent ValidityA construct measured by 2 methods should produce a moderate to strong correlation between the 2 measures (e.g., a person's anxiety determined by a questionnaire and a person's anxiety determined by a structured interview).Discriminant ValidityScores on the measure are not related to other measures that are theoretically different (if Grit is theoretically different from Conscientiousness, the correlation between these measures should not be strong)Nomological NetworkAn approach used as part of the process of gathering evidence of construct validity of educational and psychological measures. Similar to the research process, relationships based on theory between measures that the new measure should relate to and measures it should not relate to are tested.Reliability

During a 4-month-long drought, the water level in a lake changed by
−3 1/2 feet. The water level changed at the same rate each month.
What is amount the water level changed in 1 month?

Answers

In 4 months, the water level changed in the lake by -3.5 ft.
We want to know the change in one month knowing that the change is the same for all months.
To do that, we can simply do a cross multiplication as follows:
change per month=(1*-3.5)/4 = -0.875 ft

Answer:

-7/8

Step-by-step explanation:

i did the 3.15 Unit Test

a real estate developer is looking to find help fund a new condo complex.he promises 145% return on investment in four years. if youre interested in investing $30,000 and the developer follows through on his promise, how much money will you get back in four years?

Answers

145%=1.45 in decimal form
30000 (1.45)=43500 investment earning
Total received =30000+43500=73500

Why i hundred 4 tens and 14 tens name the same number

Answers

1 hundred can also be 10 tens so when you add 10 tens and 4 tens you 14 tens and that is the same thing as 14 tens.

Graph the following lines and write the equation in slope-intercept form. Through the point (−8,1) with a slope of 3.

Answers

m = 3
y = 3x + b
use the point to solve for y-intercept b
1 = 3(-8) + b
1 = -24 + b
1 + 24 = b
25 = b

equation
y = 3x +25

Given the number 456789abh, list out its byte value in little-endian order

Answers

The given 32-bit value is 456789ab in hexadecimal notation.
Each byte uses two hex digits.
The 4 bytes contained in the number are
45 67 89 ab.

Little-endian order stores the least significant bytes first in the smallest memory address.
Therefore the storage in little-endian order is
ab
89
67
45

Answer:
The byte values are ab, 89, 67, 45

The little-endian byte value of 456789abh is 0xab896745, listed in reverse order of its hexadecimal representation.

To represent the number 456789abh in little-endian byte order, we break it into bytes (8 bits each) and reverse their order:

456789abh = 0x456789ab

In little-endian order:

- 0xab

- 0x89

- 0x67

- 0x45

So, the little-endian byte value of 456789abh is 0xab896745.

How many numbers are 10 units from 0 on the number line? Type your answer as a numeral.How many numbers are 10 units from 0 on the number line?

Answers

2 numbers are 10 units from 0. If you start from zero and count 10 units to the right, you should be at a positive number. But, you can also move 10 units to the left. If you do this, you should be at a negative number that is ALSO 10 units away from 0, just in a different direction than positive number. both are 10 units from 0. There always 2 numbers, one 10 units to the right of zero, and one 10 units to the left of zero. Hope this helped! Tell me if I'm wrong or right. :)

Answer:

10 number

Step-by-step explanation:

A number line is a straight horizontal line which shows integers. Center of number line is 0.

Left side of 0 is negative integers or numbers

Right side of 0 is positive integers or numbers

" 10 units from 0 on number line"

It would be either left side or right side.

So, number will be -10 or 10.

Please have a look in attachment for number line.

So, 10 number from 0 on number line either left or right side.

3.74 rounded to the nearest
hundredth

Answers

3.75 is 3.74 rounded to the nearest hundredth

The answer is 3.74. Hope this helps :)

If the force is f=-30 units and the acceleration is a=6 units, find the mass, m

Answers

According to Newton's law:
Force = mass * acceleration
The force is given as -30 units (the negative sign only indicates the direction)
The acceleration is given as 6 units

Substitute is the above equation to get the mass as follows:
30 = 6*mass
mass = 30/6 = 5 units

Use the diagram to find the value of x?
147 32 33 150

Answers

what is the diagram?

In calculating the monthly payment for a five-year loan, what value should be used for n, the number of periods over which the loan is repaid, as it appears in the following formula? 2007-10-03-00-00_files/i0060000.jpg a. 5 b. 12 c. 60 d. 120

Answers

Answer:

The answer is: c. 60.

Step-by-step explanation:

To calculate the monthly payment for 5 years, the 12 months of 1 year should be multiplied by the 5 years of the duration, which is equal to 60 = 5 x 12.

The answer is: c. 60.

The force of an object (f) is equal to its mass (m) times its acceleration (a). Thus, the formula for calculating force is f = ma.

Based on this information, which of the following equations would be used to calculate acceleration?

A. a = fm B. a = f + m C. a = f − m D. a = f ÷ m

Answers

Your answer would be D. Bc you haven't divide a from b to get f on the other side if the equation.

Answer:

D. [tex]a=f\div m[/tex].

Step-by-step explanation:

We are given that force of an object and we have to find the equation would be used to calculate the acceleration

Mass of object=m

Acceleration of an object= a

Force of an object=f

We are given that force of an object is equal to its mass times its acceleration.

Therefore , the formula for calculating force

f=ma

Because we are given this formula

Now , we have find the equation which is used to calculate acceleration

Then by division property of equality we have

[tex]a=f\div m[/tex]

Hence, the equation would be used to calculate acceleration [tex]a=f\div m[/tex].Therefore, option D is true.

graph of the quadratic function f(x)=‒(x+4)(x‒6) is shown on the coordinate grid below.

Which statement is not true?
A.
The maximum of this function occurs when y=25.
B.
The function increases in the interval 1 to 6.
C.
The has a zero at (‒4,0).
D.
The function positive in the interval ‒4 to 6.

Answers

the correct answer is c because zero wasnt incluing and it said positive 4 to -6

Answer:

Option B is not true.

Step-by-step explanation:

The quadratic function is f(x) = -(x + 4)(x - 6)

Now we check each option given

Option A.

It is clear from the graph function is maximum at y = 25.

TRUE.

Option B.

Function increases in the interval 1 to 6.

Let's check this at x = 2 and x = 3

f(2) = -(2 + 4)(2 - 6)

= -(6)(-4)

= 24

f(3) = -(3 + 4)(3 - 6)

= - (7)(-3)

= 21

So we find this function is decreasing in this interval.

So the given option is FALSE.

Option C.

The function has a zero at (-4, 0)

f(-4) = -(-4 + 4)(-4 + 6) = 0

So the function has a zero at (-4, 0).

Option is True.

Option D.

The function is positive in the interval -4 to 6

f(x) = -(x + 4)(x - 6)

f(-3) = -(-3 + 4)(-3 - 6)

= -(1)(-9)

= 9

f(0) = -(0 + 4)( 0 - 6)

= 24

Therefore, this function is positive in this interval so the option is TRUE.

Option B is not true.

Anyone knows the answer

Answers

The answer is 16,300. To get the answer, you just move the decimal over 4 places to the right and add your zeros in.

hopefully this helps

It would be the 3rd one hope this helps good luck

A town's population is 43,200. About 100 people move out of the town each month. Each month, 125 people on average move into town. A nearby town has a population of 45,000. It has no one moving in and an average of 200 people moving away every month. In about how many months will the populations of the towns be equal?

Answers

It will take 12 months.

Indicate the equation of the given line in standard form. The line that is the perpendicular bisector of the segment whose endpoints are R(-1,6) and S(5,5)

Answers

well the line that bisects RS, will cut RS in two equal halves, therefore, that line will cut RS perpendicularly at the midpoint of RS.

now, what the dickens is the midpoint of RS anyway?

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) R&({{ -1}}\quad ,&{{ 6}})\quad % (c,d) S&({{ 5}}\quad ,&{{ 5}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left( \cfrac{5-1}{2}~~,~~\cfrac{5+6}{2} \right)\implies \stackrel{midpoint}{\left(2~~,~~\frac{11}{2} \right)}[/tex]

so, we know that perpendicular line, will have to go through (2, 11/2)

now, a perpendicular line to RS, will have a negative reciprocal slope to it. Well, what is the slope of RS anyway?

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -1}}\quad ,&{{ 6}})\quad % (c,d) &({{ 5}}\quad ,&{{ 5}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{5-6}{5-(-1)}\implies \cfrac{5-6}{5+1}\implies -\cfrac{1}{6}[/tex]

and let's check the reciprocal negative of that,

[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -\cfrac{1}{6}\\\\ slope=-\cfrac{1}{{{ 6}}}\qquad negative\implies +\cfrac{1}{{{ 6}}}\qquad reciprocal\implies + \cfrac{{{ 6}}}{1}\implies 6[/tex]

so, then, what's is the equation of a line whose slope is 6, and goes through 2, 11/2?

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 2}}\quad ,&{{ \frac{11}{2}}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 6 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-\cfrac{11}{2}=6(x-2) \\\\\\ y-\cfrac{11}{2}=6x-12\implies -6x+y=-12+\cfrac{11}{2}\implies \stackrel{\textit{standard form}}{-6x+y=-\cfrac{13}{2}}[/tex]

Final answer:

The equation of the perpendicular bisector of the segment with endpoints R(-1,6) and S(5,5) is found by calculating the midpoint, slope, and using the negative reciprocal for the perpendicular slope. It is then written in point-slope form and converted to standard form, resulting in 12x - 2y = 13.

Explanation:

To find the equation of a line that is the perpendicular bisector of a segment with endpoints R(-1,6) and S(5,5), we need to take the following steps:

Determine the midpoint of the segment RS which will be a point on our bisector.Calculate the slope of the line segment RS.Find the negative reciprocal of the slope from step 2, which will give us the slope of our perpendicular bisector.Write the equation of the bisector line using the point-slope form and then convert it into standard form.

The midpoint of RS is given by ((-1+5)/2, (6+5)/2) = (2, 5.5). The slope of RS is (5-6)/(5-(-1)) = -1/6. The negative reciprocal of -1/6 is 6. Thus, the slope of our bisector is 6.

Using the point-slope form with the midpoint, y - 5.5 = 6(x - 2). Expanding and rearranging to standard form, we get:

6x - y = 12 - 5.5 -> 6x - y = 6.5.

Multiplying through by 2 (to clear the decimal), we obtain:

12x - 2y = 13, which is the standard form equation of the perpendicular bisector of segment RS.

If a refrigerator is a heat pump that follows the first law of thermodynamics, how much heat was removed from food inside of the refrigerator if it released 492J of energy to the room? Joules

Answers

First, we need to define the first law of thermodynamics. This law states that in an isolated system, energy can neither be created nor destroyed, it can just be transformed from one form to another.

Based on this, if we assume that the refrigerator is and isolated system, then if 492 Joules of energy was released into the room, this means that 492 Joules of energy (heat) was removed from food inside the refrigerator.

In triangle FGH, GJ is an angle bisector of ∠G and perpendicular to FH.

What is the length of FH?

___ units

Answers

The answer you're looking for is:
16. I know this for certain.

Remember to mark Brainliest if this was helpful!

we know that

in the right triangle FGJ

[tex]cos(FGJ)=\frac{GJ}{FG}= \frac{GJ}{3x-8}[/tex] ----> equation A

in the right triangle GJH

[tex]cos(JGH)=\frac{GJ}{GH}= \frac{GJ}{16}[/tex] ----> equation B

m∠(FGJ)=m∠(JGH) ------> because GJ is an angle bisector of ∠G

equate equation A and equation B

[tex]\frac{GJ}{3x-8}=\frac{GJ}{16}\\ 3x-8=16\\3x=24 \\x=8\ units[/tex]

that means

[tex]FG=3*8-8=16\ units[/tex]

[tex]FG=GH[/tex]-------> the triangle FGH is an isosceles triangle

hence

[tex]FJ=JH\\FJ=8\ units[/tex]

[tex]JH=8\ units[/tex]

[tex]FH=FJ+JH=8+8=16\ units[/tex]

therefore

the answer is

[tex]FH=16\ units[/tex]

Describe sets of two or more matching integer cards that satisfy the criteria in each part below:
a. Cards increase the score by eight points.
b. Cards decrease the score by 9 points.
c. Removing cards that increase the score by 10 points.
d. Positive cards that decrease the score by 18 points.

Answers

What cards do you have to show us

Answer:

a. Removing two (-4)'s

b. Picking up three (-3)'s or removing three 3's

c. Removing two (-3)'s and one (-4)'s

d. Removing three 5's and one 3's

Step-by-step explanation:

Cards available: 5, -3, -4, & 3

a. Score can be increased picking up positive cards or removing negative cards.

b. Score can be decreased picking up negative cards or removing positive cards.

c. As stated before, in order to increase the score removing cards, positive cards have to be removed.

d. As stated before, in order to decrease the score with positive cards, those cards have to be removed.

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