You borrow $2250 at 4.8% compounded weekly for tuition. While you do not have to make payments for the 5 years that you are in school, the interest is compounding. What is your loan balance after the 5-year grace period (if you've made no payments)?

Step-by-step explanation:

In ascending order

100 , 102 , 103 , 106, 109

No of data (N) = 5

Now

Position of median

= ( N + 1) /2 th item

=( 5+1 )/2 th item

= 6 / 2 th item

= 3rd item

Therefore exact median = 103

Hope it will help you :)

Answer:

103

Step-by-step explanation:

100,102,103,106,109

Median position: (n+1)/2

(5+1)/2 = 3rd value

Median = 103

Answer:

Answer: A

Step-by-step explanation:

The scenario best correlates with the principle of 'Acceptability' in money characteristics, where the Magic cards are accepted in place of traditional currency for trades on IMagicCards.com.

Magic Cards as Currency

The scenario you've described involves the trading of Magic: The Gathering cards on IMagicCards.com. This website uses the cards themselves as a form of currency instead of traditional money. Assessing the relation to characteristics of money, this system best correlates with Acceptability. Acceptability is a key attribute of money, signifying that it must be widely accepted for the purchase of goods and services. In this context, the acceptance of Magic cards for trades is equivalent to the principle of acceptability in currency.

The other options do not seem to fit as appropriately in this case. Portability involves the ease with which units of currency can be transported for use in purchasing or trade. Divisibility refers to the ability of money to be divided into smaller units without loss of value. Durability means the currency must withstand the physical wear and tear. Stability pertains to the value of the money remaining relatively stable over time.

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Answer:

33.333%.

Step-by-step explanation:

Take the cost changed ($4) and divide it by it's normal price ($12).

$4/$12 = .33333

Multiply that by 100 to get its percent. 33.333%

Answer:

- 33.3%

Step-by-step explanation:

You calculate percent change by dividing the change by the absolute value of the original. In this instance, it would be -4/12 which equals -0.3333. Multiply that by 100 and you get the percent.

(1) 132.67 square meters

(2) 379.94 square meters

Step-by-step explanation:

A barn is in the shape of a rectangle with each corner angle a right angle.

[tex] \therefore Central\: \angle \:(\theta) =90°[/tex]

Since, goat is tied at a corner of the barn, so she would be able to graze the grass of sector of circle with radius (r) = 13 m.

Area of field grazed by goat = area of sector of circle

[tex] = \frac{ \theta}{360 \degree} \times \pi {r}^{2} \\ \\ = \frac{90 \degree}{360 \degree} \times 3.14 \times {13}^{2} \\ \\ = \frac{1}{4} \times 3.14 \times 169\\ \\ = \frac{1}{4} \times530.66 \\ = 132.665 \\ = 132.67 \: {m}^{2} [/tex]

[tex] (2) \\ similarly \: for \: r \: = 22 \: m \\ area \: of \: sector = 379.94 \: {m}^{2} [/tex]

Prism B has larger volume than Volume of prims A.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

Volume has units of cube example meter³,cm³, etc.

Given that;

Prism A has a length of 2 units, height of 7 units, and width of 1 unit. Prism B has a length of 3 units, height of 2 units, and width of 3 units.

Since, The volume of the rectangular prism is given as,

V = length × height × width

Put length as 2 unit cubes, height as 7 unit cubes, and width as 1 unit cubes.

For prism A;

V = 2 x 7 x 1 = 14 units³.

Put length as 3 unit cubes, height as 2 unit cubes, and width as 3 unit cubes.

For prism B;

V = 3 x 2 x 3 = 18 units³.

Hence, Prism B has larger volume than Volume of prims A.

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Answer:

I think it's 55.

Step-by-step explanation:

11-n/5

n=11*5

n=55

Answer:

[tex]\frac{n-11}{5}[/tex]

Step-by-step explanation:

1) Subtract 11 from n to get [tex]n-11[/tex]   You cannot find a solution for it because there is no value for n.

2) You divide that by 5 so you would just put n-11 over 5 to create a fraction that would look like [tex]\frac{n-11}{5}[/tex]

I am not sure if this is what you were asking but this is the most I can do for you with the information that you gave.

Answer:

Correct option is (A). H₀: [tex]\mu_{d}[/tex] = 0.5

Step-by-step explanation:

The (1 - α)% confidence interval for a population parameter can be used to determine whether to reject a null hypothesis or not.

The decision rule is:

If the (1 - α)% confidence interval for a population parameter consists of the null value of the parameter then the null hypothesis will be accepted or else it will be rejected.

A hypothesis test is performed to determine the difference between the ideal and actual heights of college males.

The 95% confidence interval for the mean difference, [tex]\mu_{d}[/tex] is:

CI = (0.8, 2.2)

The four null hypothesis provided are:

The 95% confidence interval for the mean difference consists of the value, 1.0, 1.5 and 2.0.

But it does not consist the value 0.5.

So, the null hypothesis that can be rejected is:

H₀: [tex]\mu_{d}[/tex] = 0.5

Thus, the correct option is (A).

Based on the 95% confidence interval given, we can only reject null hypothesis H0: μd= 0.5. The rest of the null hypotheses fall within the interval and therefore, cannot be rejected.

Based on the 95% confidence interval, which ranges from 0.8" to 2.2", we are interested in whether 0 falls within this range. When it falls within this range, we cannot reject the null hypothesis. Going through the provided null hypotheses, we can reject the null hypothesis which falls outside the confidence interval.

Considering:
A. H0: μd= 0.5
B. H0: μd= 1.0
C. H0: μd= 1.5
D. H0: μd= 2.0

Only hypothesis A falls outside the confidence interval, thus we can reject null hypothesis H0: μd= 0.5. The null hypotheses stating μd= 1.0, μd= 1.5, and μd= 2.0 fall within this range and therefore, cannot be rejected based on this confidence interval.

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m=6.50t

6.50 per ticket so you multiply 6.50 by t. The money collected is the answer to the equation. Hope this helps!

Answer:

The calculated value t = 5.608 > 2.3988 at 0.1 level of significance with 53 degrees of freedom.

The null hypothesis is rejected at 0.1 level of significance

The company do not believes that there has been an INCREASE in the life expectancy of its D size batteries

Step-by-step explanation:

Step(i):-

Given data the size of sample n=54

Given "D" size batteries produced by MNM Corporation have had a life expectancy of 85.8 hours

therefore mean of Population μ = 85.5 hours

Given a sample of 54 batteries showed an average life of 88.7 hours with a standard deviation of 3.8 hours

The mean of the sample x⁻ = 88.7 hours

The standard deviation of the sample (S) = 3.8 hours

Step(ii):-

Null hypothesis : H₀:μ > 85.5 hours

Alternative hypothesis: H₁:μ < 85.5 hours

Level of significance : ∝= 0.1

Degrees of freedom γ =n-1 = 54-1 =53

The test statistic

[tex]t= \frac{x^{-}-u }{\frac{S}{\sqrt{n} } }=\frac{88.7-85.8}{\frac{3.8}{\sqrt{54} } }[/tex]

t = 5.608

The tabulated value t = 2.3988 at 0.1 level of significance with 53 degrees of freedom.

Conclusion:-

The calculated value t = 5.608 > 2.3988at 0.1 level of significance with 53 degrees of freedom.

The null hypothesis is rejected at 0.1 level of significance

The company do not believes that there has been an INCREASE in the life expectancy of its D size batteries

Answer:

[tex]\hat p  \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]

The mean is given by:

[tex] \mu_{\hat p} = 0.55[/tex]

And the deviation:

[tex] \sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161[/tex]

Step-by-step explanation:

For this case we assume that the true population proportion of Americans do not know that GOP stands for Grand Old Party is 0.55 and we select a random sample of n = 953 americans

For this case we assume that we satisfy the conditions to use the normal approximation for [tex]\hat p[/tex]

1) np >10 , n(1-p)>10

2) Independence

3) Random sample

4) The sample size is less than 10% of the population size

We assume that all the conditions are satisfied and the distribution for [tex]\hat p[/tex] would be:

[tex]\hat p  \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]

The mean is given by:

[tex] \mu_{\hat p} = 0.55[/tex]

And the deviation:

[tex] \sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161[/tex]

Answer:

38 > 36

it is true it shows that 38 is greater than 36

Answer:

1,600

Step-by-step explanation:

3000/75=40

40*40=1,600

Final answer:

The best prediction for the number of people who will vote for Mr. Beston out of 3,000 voters is found through a simple proportion, resulting in an estimated 1,600 votes for Mr. Beston.

Explanation:

The question asks for a prediction of the number of people who will vote for Mr. Beston if 3,000 people vote, based on the results of a survey where 40 out of 75 people indicated they would vote for him. To find this prediction, we use a simple proportion. We set up a ratio of the number of people who plan to vote for Mr. Beston to the total number surveyed and set this equal to the unknown number of people who will vote for Mr. Beston out of 3,000 total voters.

The ratio or survey proportion is 40/75. We set up the following proportion to find the predicted number of votes:

40/75 = x/3000,

where x is the number we want to find. By cross-multiplying, we get:

40 * 3000 = 75 * x,

which simplifies to:

120,000 = 75x.

Now, we divide both sides by 75 to isolate x:

x = 120,000 / 75,

x = 1600.

Therefore, the best prediction is that 1,600 people out of 3,000 will vote for Mr. Beston.

Answer: the character of king Henry, or Harry

Step-by-step explanation:

Answer:

Because our p-value of .023 is lower than the alpha-level of .05, we reject the null hypothesis. There is sufficient evidence to conclude that the proportion of subjects who have the necessary qualities is less than .2. Our test provided a statistically significant result.

Answer:

the answer is 80%

Step-by-step explanation:

4/5 = 80%

Answer:

in fraction form that is 4/5   or .8 chance of getting a blue marble

Step-by-step explanation:

because you divide  the number of possible  winning out comes 4 marbles  by the total  event 5 marbles

Answer:

pic not their put plz so i can answer

Step-by-step explanation:

Answer:

The central line of the p-chart is 0.05.

Step-by-step explanation:

In statistical quality control, the p-chart is a form of control chart used to observe the proportion of non-conforming or defective components in a random sample, where the sample proportion of defective items is defined as the fraction of the number of defective units to the size of the sample, n.

The central line of the p-chart is given by:

[tex]CL=\frac{\sum np}{\sum n}[/tex]

It is provided that:

The sample selected from a shipment for inspection every day is of size, n = 50.

The average percentage of incorrect shipments is 5%, i.e. p = 0.05.

Compute the number defective units in the sample as follows:

[tex]np=50\times \frac{5}{100}[/tex]

Compute the central line of the p-chart as follows:

[tex]CL=\frac{\sum np}{\sum n}[/tex]

      [tex]=\frac{5\times 50}{100\times 50}\\[/tex]

      [tex]=0.05[/tex]

Thus, the central line of the p-chart is 0.05.

The center line for a p-chart is calculated as the average percentage of defects across all samples, which in this case is 5%.

The center line for a p-chart is calculated as the average percentage of defects across all samples.

In this case, the average percentage of incorrect shipments is 5%.

Hence, the center line for the p-chart in this scenario would be 5%.

Complete question:

A manufacturer has determined that a model of its washing machine has an expected life that is Exponential with a mean of four years to failure and irrelevant board burn-in period. He wants to testthe system and complete data collection. Find the probability that one of these washing machines will have a life that ends: (Note you can find the reliability of the washing machine life)

a) After an initial four years of washing machine service

b) Before four years of washing machine service are completed

c) Not before six years of washing machine service.

Answer:

a) 0.3679

b) 0.6321

c) 0.2231

Step-by-step explanation:

Given:

Mean, u= 4

/\ = 1/u

= 1/4 = 0.25

The cummulative distribution function, will be:

For x≥0,

[tex] F(x) = 1 - e^-^0^.^2^5^X[/tex]

[tex]P(x<X) = F(X)[/tex]

a) After an intial four years:

[tex]P(x>4) = 1-(1-e^-^0^.^2^5^*^4^.^0)[/tex]

P(x>4) = 0.3679

b) Before four years:

[tex]P(x<4) = 1-(e^-^0^.^2^5^*^4^.^0)[/tex]

P(x<4) = 0.6321

c) Not before 6 years:

[tex]P(x>6) = 1-(1-e^-^0^.^2^5^*^4^.^0)[/tex]

P(x>6) = 0.2231

Answer:

? necesitamos  más  información..  ¿dónde están los fracciones?

Step-by-step explanation:

Given:

In the given ΔEFG,

EP = FP and GQ = FQ

Again,

EP = [tex]4y+2[/tex]

FP = [tex]2x[/tex]

FQ = [tex]3x-1[/tex]

GQ = [tex]4y+4[/tex]

PQ = [tex]x+2y[/tex]

To find the perimeter of ΔEFG.

Formula

In this given triangle, EG║PQ and EG = [tex]\frac{1}{2}[/tex]PQ

Now,

By given condition,

[tex]2x = 4y+2[/tex] ----- (1)

[tex]3x-1 =4y+4[/tex]---------(2)

From (1) we get, [tex]4y = 2x-2[/tex]

Putting this value into (2) we get,

[tex]3x-1 = 2x-2+4[/tex]

or, [tex]x = 3[/tex]

From (1) we get,

[tex]4y = 2(3)-2[/tex]

or, [tex]4y = 4[/tex]

or, [tex]y = 1[/tex]

So,

EF = [tex]2x+4y+2[/tex] = [tex]2(3)+4(1)+2 = 12[/tex] unit

FG = [tex]3x-1+4y+4 = 3(3)-1+4(1)+4 = 16[/tex] unit

PQ =[tex]3+2(1) = 5[/tex] unit

EG = [tex]2(5) = 10[/tex] unit

The perimeter of ΔEFG = EF+FG+EG = 16+10+12 unit = 38 unit

Hence,

The perimeter of the given triangle is 38 unit.

The perimeter of the ΔEFG when EP = FP and GQ = FQ should be 38 units.

Since

EP = 4y + 2

FP = 2x

FQ = 3x - 1

GQ = 4y + 4

PQ = x + 2y

So,

2x = 4y +2 ..(1)

4x - 1 = 4y + 4........(2)

So,

3x - 1 = 2x - 2 + 4

y = 1

Now

= EF + FG + FG

= 16 + 10 + 12

= 38 units

hence, The perimeter of the ΔEFG when EP = FP and GQ = FQ should be 38 units.

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Given:

Given that the side of the regular polygon is 16 feet.

We need to determine the area of the polygon.

Area of the polygon:

The area of the polygon can be determined using the formula,

[tex]Area =\frac{s^2 n}{4 \ tan \frac{180}{n}}[/tex]

where n is the number of sides,

s is the side length.

Substituting n = 3 and s = 16, we get;

[tex]Area =\frac{16^2 (3)}{4 \ tan \frac{180}{3}}[/tex]

Simplifying, we get;

[tex]Area =\frac{(256) (3)}{4 \ tan \ 60}[/tex]

[tex]Area = \frac{768}{6.928}[/tex]

Dividing, we get;

[tex]Area = 110.85[/tex]

Rounding off to the nearest tenth, we have;

[tex]Area = 110.9[/tex]

Thus, the area of the regular polygon is 110.9 square units.

Problem 1

----------------

Work Shown:

There are n = 6 red marbles and r = 5 ways to pick them (order does not matter). Use the combination formula to find that

n C r = (n!)/(r!(n-r)!)

6 C 5 = (6!)/(5!*(6-5)!)

6 C 5 = (6!)/(5!*1!)

6 C 5 = (6*5!)/(5!*1!)

6 C 5 = (6)/(1!)

6 C 5 = (6)/(1)

6 C 5 = (6)/(1)

6 C 5 = 6

Now repeat for n = 6+9+8 = 23 and r = 5

n C r = (n!)/(r!(n-r)!)

23 C 5 = (23!)/(5!*(23-5)!)

23 C 5 = (23!)/(5!*18!)

23 C 5 = (23*22*21*20*19*18!)/(5!*18!)

23 C 5 = (23*22*21*20*19)/(5!)

23 C 5 = (23*22*21*20*19)/(5*4*3*2*1)

23 C 5 = (4037880)/(120)

23 C 5 = 33649

We have 6 ways of getting what we want (picking five red marbles) out of 33649 ways total (to get five marbles of any color). Again order does not matter.

Divide: 6/33649 = 0.00017831139112

This rounds to 0.0002 when rounding to four decimal places.

=========================================

Problem 2

----------------

Work Shown:

There are 6 C 2 = 15 ways to pick 2 red marbles

There are 17 C 3 = 680 ways to pick 3 non-red marbles.

There are 15*680 = 10,200 ways to pick 5 marbles such that 2 are red, the rest aren't.

There are 33649 ways to select 5 marbles where color doesn't matter

So,

10200/33649 = 0.30312936491427

which rounds to 0.3031

=========================================

Problem 3

----------------

Work Shown:

There are 17 marbles that aren't red, so there are 17 C 5 = 6188 ways to pull out five of them

This is out of 33649 ways to pull out five marbles in general.

6188/33649 = 0.18389848138131

which rounds to 0.1839

The probability of drawing all marbles red is extremely low (0.0002), while the probability of drawing exactly two red marbles is much higher (0.2865). If no red marbles are drawn, the probability is 0.1839.

To solve these problems, we will use the basic principles of probability and combinations, since we are dealing with the probability of drawing marbles without replacement.

1. Probability that all marbles are red

We have a total of 23 marbles (6 red, 9 white, 8 blue). Since we're drawing 5 marbles without replacement, to get the probability that all marbles are red, we need to calculate the combinations of choosing 5 out of 6 red marbles and divide that by the combinations of choosing 5 out of all 23 marbles.

Probability = (⁶C₅) / (²³C₅) = 6/33649 = 0.0002

2. Probability that exactly two of the marbles are red

Here, we want two red marbles and the remaining three to be non-red (either white or blue). We calculate this by multiplying the combination of choosing 2 reds out of 6, 3 non-reds out of 17 (total marbles minus red marbles), and divide by the total combinations of choosing 5 out of 23.

Probability = (⁶C₂ × ¹⁷C₃) / (²³C₅) = (15 × 680) / 33649 = 0.2865

3. Probability that none of the marbles are red

To find the probability of drawing no red marbles, we only consider the white and blue ones, so we want all 5 to be from the 17 non-red marbles.

Probability = (¹⁷C₅) / (²³C₅) = 6188 / 33649 = 0.1839

To find the probabilities of a randomly selected U.S. adult using social media and being aged 18-29, we can use probability concepts and the given information.

To solve this problem, we can use the concept of probability. Let's define the following events:

From the information given, we have P(A' ∩ B') = 35%, P(A' ∩ B) = 0, P(A ∩ B') = 67.2%. We need to find the probabilities P(A) and P(B).

Therefore, the probability that a randomly selected U.S. adult uses social media is 102.2%, the probability that a randomly selected U.S. adult is aged 18-29 is 22%, and the probability that a randomly selected U.S. adult is 18-29 and a user of social media is 67.2%.

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a. Probability of a randomly selected U.S. adult using social media is 45.2%.

b. Probability of a randomly selected U.S. adult being aged 18-29 is 65%.

c. Probability of a randomly selected U.S. adult being 18-29 and a user of social media is approximately 29.38%.

a. Probability a randomly selected U.S. adult uses social media:

Probability of being 18-29 or use social media = 67.2%

Percentage of US adults aged 30 and older = 78%

Thus, percentage of US adults aged 18-29 = 100% - 78% = 22%

Probability of using social media = 67.2% - 22% = 45.2%

b. Probability of a randomly selected U.S. adult being aged 18-29:

Percentage of adults not using social media = 35%

Thus, percentage of adults aged 18-29 = 100% - 35% = 65%

c. Probability of a randomly selected U.S. adult being 18-29 and a user of social media:

Probability of using social media = 45.2%

Probability of being 18-29 = 65%

Probability of being 18-29 and using social media = 0.452 * 0.65 = 29.38%

Answer:

At t=1, Rate of Change=-36.86

At t=10 hours, Rate of Change =-0.0088

Step-by-step explanation:

The function which describes the number of facts of a certain type which are remembered after t hours is given as:

[TeX]f(t)=\frac{85t}{99t-85}[/TeX]

To determine the Rate of Change at the given time, we first look for the derivative of f(t).

Applying quotient rule:

[TeX]f^{'}(t)=\frac{-7225}{{\left( 85 - 99\,t\right) }^{2}}[/TeX]

At t=1

[TeX]f^{'}(1)=\frac{-7225}{(85-99)^{2}}[/TeX]

=-36.86

At t=10 hours

[TeX]f^{'}(10)=\frac{-7225}{(85-99(10))^{2}}[/TeX]

=-0.0088

The rate of change of the function is calculated by finding its derivative and evaluated by substituting the respective hours (1 hour and 10 hours). The rate of change after 1 hour is approximately -106.25, implying a decline per hour, and after 10 hours is approximately -0.918, indicating a slower rate of decline per hour.

The rate of change of a function is calculated by finding the derivative of the function. The derivative of a function gives the rate of change of the function at any given point. Let's calculate the derivative of the function f(t) = 85 t / (99 t - 85).

We get f'(t) = (85*(99 t - 85) - (85 t)*99) / (99 t -85)² = (-850)/ (99 t - 85)². This is the rate of change of the function f(t).

To find the rate of change after 1 hour and 10 hours, substitute t = 1 and t = 10 into f'(t).

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Answer: $11,155

Step-by-step explanation: For this problem, first we will use the "Simple Interest" equation to find the total interest earned after three years.

First, convert 3.85% to a decimal, 0.0385.

I, interest = 10,000 x 0.0385 x 3

I = 1,155

Now add the total interest $1,155 to the total deposit $10,000.

1,155 + 10,000 = $11,155

By using  the formula for amount of Compound Interest the result is

Ending balance after 3 years = $11224.29

What is compound Interest?

If the interest on a certain principal increases exponentially rather than  linearly on a certain rate over a certain period of time, then the interest obtained is known as compound interest.

If the principal be P, rate is r%, time is n years,

Amount = [tex]P(1 + \frac{r}{100})^n[/tex]

CI = Amount - Principal

Here,

Principal = $10000

Rate = 3.85%

Time = 3years

Amount =

[tex]10000(1+\frac{3.85}{36500})^{3\times 365}\\10000(1 + \frac{385}{3650000})^{1095}\\[/tex]

11224.29

Ending balance after 3 years = $11224.29

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Answer:

The socks cost $2.44 per pair

Step-by-step explanation:

Everything costs $21.85 in total. The given values are $6.75 for each jersey (which adds to make both jerseys together make $13.50). There is also a given value of $1.03 for total sales tax. If you add the jerseys and tax, you get $14.53. Subtract that from $21.85 to get $7.2. That is the total for all three pairs of socks, so divide that by three and you get $2.44 for each pair of socks :)

Answer:

46.142857143

Step-by-step explanation:

10×2+(30-15)÷7+3×8

=10×2+15÷7+3×8

=20+15÷7+3×8

=20+2.142857143+3×8

=20+2.142857143+24

=46.142857143

Answer:

We need a sample of size at least 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Assume that we want 95% confidence that the proportion from the sample is within two percentage points of the true population percentage.

We need a sample of size at least n.

n is found when [tex]M = 0.02[/tex]

We don't know the exact proportion, so we use [tex]\pi = 0.5[/tex], which is the case for which we are going to need the largest sample size.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.02\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.02}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.02})^{2}[/tex]

[tex]n = 2401[/tex]

We need a sample of size at least 2401.

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401[/tex]  

And rounded up we have that n=2401

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.02[/tex] or 2% points and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

We can use an prior estimation for p [tex]\hat p=0.5[/tex]. And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401[/tex]  

And rounded up we have that n=2401

Answer:

The common difference is 0.38

Step-by-step explanation:

If you look at the data, you can find that the y-value is getting 0.38 added to it. 24 + 0.38 is 24.38. 24.38 + 0.38 is 24.76. 24.76 + 0.38 = 25.14. Therefore, the common difference is 0.38.

Answer:

0.38

Step-by-step explanation:

It was right when I did it on flvs.